Excerpt

## Table of contents

List of tables

List of figures

List of abbreviations

List of symbols

1 Introduction

1.1 The problem

1.2 Research gaps and objectives

1.3 Structure and methods

2 Design possibilities of structured equity products

2.1 Introduction

2.2 Overview of structured equity products

2.2.1 Capital protected certificates

2.2.2 Yield enhancement certificates

2.2.3 Participation certificates

2.3 Design calculus

2.3.1 Budget constraints

2.3.2 Risk-neutral option theory

2.3.3 Base model

2.3.3.1 Interest rate proceeds as budget constraints

2.3.3.2 Dividend proceeds as budget constraints

2.3.4 Product launch possibilities

2.3.4.1 Capital protected certificates

2.3.4.2 Yield enhancement certificates

2.3.4.3 Participation certificates

2.4 Design preferences of issuers

2.4.1 Products with budget constraints

2.4.1.1 Budget and option price sensitivities

2.4.1.2 Margin ceiling

2.4.1.3 Design of n-year products

2.4.2 Products without budget contraints

2.3.2.1 Premium income

2.3.2.2 Design of n-year products

2.5 Result

2.6 Discussion

3 Hedging discipline of issuers

3.1 Introduction

3.2 Limit policy

3.3 Limit utilization

3.3.1 Position limits at issue day

3.3.2 Dynamic loss limits

3.3.3 Intraday stop loss limits

3.3.4 Methods to measure option risk

3.3.5 Limit setting for option trade positions

3.3.6 Simulating option risk

3.4 Research design

3.4.1 Option theoretical approach

3.4.1.1 The cost of limit violations

3.4.1.2 Result of experiment

3.4.2 Historical simulation

3.4.2.1 Historical data set

3.4.2.2 Results of historical simulations

3.5 Result

3.6 Discussion

4 Structured equity products from the retail client’s perspective

4.1 Introduction

4.2 Choice under risk

4.2.1 Departure from expected utility theory (EUT)

4.2.2 Functional forms of probability weighting functions

4.2.2.1 One parameter probability weighting functions

4.2.2.2 Two parameter probability weighting functions

4.2.2.3 Delay dependent probability weighting functions

4.3 Desirability study for structured equity products

4.3.1 The model

4.3.2 Research design

4.3.2.1 Desirability of stocks and risk-free assets

4.3.2.2 Desirability of capital protected products

4.3.2.3 Desirability of yield enhancement products

4.3.2.4 Desirability of participation products

4.4 Result

4.5 Discussion

5 Conclusion

6 List of Appendices

V List of References

## List of tables

Table 1: Overview structured equity products Table 2: Issuer margins by authors Table 3: Expected shortfall and value at risk Table 4: Dynamic loss limits Table 5: Intraday stop loss limits

Table Cl: Interest and DAX volatility level for 2000 - 2016

Table Dl: Issuer margins for capital protected products w/participation

Table D2: Issuer margins for capital protected products w/cap

Table D3: Issuer margins for capital protected products w/knock-out

Table D4: Issuer margins for participation products w/outperformance

Table D5: Issuer margins for participation products w/bonus

Table D6: Issuer margins for participation products w/airbag

Table El: Anova studies for 5-year reverse convertible

Table E2: Anova studies for 1-year reverse convertible

Table F: Option risks for call options

Table G: Option risks for put options

Table HI: Dividend yield 5.00%

Table H2: Dividend yield 2.50%

Table H3: Dividend yield 0.00%

Table I: Option theoretical approach: revenue model R2 for short calls Table J: Option theoretical approach: revenue model R2 for long puts Table L: Historical simulation: revenue model R2 for short calls Table M: Historical simulation: revenue model R2 for long puts

## List of figures

Figure 1: Launch of capital prot. certificates financed by interest rates

Figure 2: Launch of capital prot. certificates financed by dividend

Figure 3: Launch of capital protected certificates with caps

Figure 4: Launch of capital prot. certificates with participation factors

Figure 5: Launch of capital protected certificates knock-out barriers

Figure 6: Launch of outperformance certificates

Figure 7: Launch of bonus certificates

Figure 8: Launch of airbag certificates

Figure 9: Capital prot. certificates with participation factor ? —? max! 38 Figure 10: Capital protected certificates with cap level ?0?? —? max!

Figure 10: Capital protected certificates with cap level XOTM ? max!

Figure 11 : Capital protected products with barrier level H —? max!

Figure 12: Outperformance certificate with factor 1 + ? —? max!

Figure 13 : Bonus certificate with barrier level of H —? max!

Figure 14: Airbag certificate with strike price of X1TM —? max!

Figure 15: Budget and put sensitivity with respect to time changes T

Figure 16: Budget and barrier option sensitivity with respect to time T

Figure 17: Budget surplus of capital protected with cap

Figure 18: Budget surplus of capital prot. certificates with participation

Figure 19: Budget surplus of capital protected certificate with barrier

Figure 20: Budget surplus of outperformance certificates.

Figure 21: Budget surplus of bonus certificates.

Figure 22: Budget surplus of airbag certificates.

Figure 23: Max. and min. coupon of 5-year reverse convertibles.

Figure 24: Max. and min. coupon of 1-year reverse convertibles.

Figure 25: Coupon levels with respect to time T.

Figure 26: Term structure of Hi Voi members.

Figure 27: Expected shortfall and trading position.

Figure 28: Number of limit violations.

Figure 29: Delta-gamma approximation.

Figure 30: Taylor Series versus scenario matrix.

Figure 31: Delta and time.

Figure 32: Measuring long call option risk.

Figure 33: Total revenue for short call options.

Figure 34: Trade revenue for long put options.

Figure 35: Loss limit violations.

Figure 36: Average revenue of short call positions.

Figure 37: Average revenue of long put positions.

Figure 39: Value function v(x) of prospect theory.

Figure 40: One parameter weighting functions.

Figure 41:Goldstein & Einhom’s two parameter weighting functions.

Figure 42: Prelec ’ s two parameter weighting function.

Figure 43:Probability weighting functions with delays.

Figure 44:Probability weighting function.

Figure 45:Decision weights.

Figure 46:Matrix of cap. prot. products & caps for rational investors.

Figure 47: Matrix of cap. prot.products & participation for rat. investors.

Figure 48: Matrix of cap. prot. products & barrier for rat. investors.

Figure 49:Matrix of cap.prot.products & caps for behavioral investors.

Figure 50: Matrix of cap. prot. products & barriers for behavioral investor.

Figure 51: Matrix of cap. prot.products & part, for behavioral investors.

Figure 52: Matrix of reverse convertibles for rational investors.

Figure 53:Matrix of protected reverse convertible for rat. investors.

Figure 54: Matrix of reverse convertible with barrier for rat. investors.

Figure 55:Matrix of reverse convertibles for behavioral investors.

Figure 56:Matrix of protected reverse convert, for behavioral investors.

Figure 57: Matrix of reverse convert. & barrier for behavioral investors.

Figure 58: Matrix of bonus products for rational investors.

Figure 59:Matrix of outperformance products for rational investors.

Figure 60: Matrix of airbag products for rational investors.

61: Matrix of bonus products for behavioral investors.

62: Matrix of outperformance products for behavioral investors. 63: Matrix of airbag products for behavioral investors.

Kl: Accumulated P/L and loss limits.

K2: Daily option price changes and stop loss limits.

N1: Short calls with 10.5% capital loss limits.

N2: Short calls with 4.00% capital loss limits.

N3: Long puts with 10.5% capital loss limits.

N4: Long puts with 4.00% capital loss limits.

## List of abbreviations

BaFIN = Bundesanstalt für Finanzdienstleistungsaufsicht

BCBS = Basel Committee on Banking Supervision

cdf = cumulative distribution function

CE = Certainty Equivalent

df = degree of freedom

EU = Expected Utility

ES = Expected Shortfall

FSB = Financial Stability Board

IOSCO = International Organisation of Securities Commissions

iTraxx = brand name for credit default swap index products

LIFFE = London International Financial Futures and Options Exchange

MaRisk = Mindestanforderungen an das Risikomanagement

MATIF = Marché à Terme International de France

max. = maximum

MIFID = Markets in Financial Instruments Directive MIFIR = Regulation on Markets in Financial Instruments min. = minimum

OMX = Optionsmäklama Exchange OTC = Over-The-Counter Market Pdf = probability density function

PRIIP = packaged retail and insurance based investment products RDU = Rank Dependent Utility

SOFFEX = Swiss Options and Financial Futures Exchange VaR = Value-at-Risk

sVAR = Value-at-Risk of a stressed period

## List of symbols

a = curvature of probability weighting function

ß = controls elevation of Prelec’s probability weighting curve

B(.) = budget function

b = discount rate

call = call option (European style)

calluo = call option, up-and-out barrier (European style)

callui = call option, up-and-in barrier (European style)

Callui = call option, up-and-in barrier (American style)

d = controls intersection in Goldstein & Einhorn’s weighting curve

(cp) = maximum coupon level

(cp) = minimum coupon level

(cp) = coupon level of reverse convertibles

escorporate corporate credit spread of unsecured bonds in %

CSissuer = credit spread of issuers in %

?= delta, option price sensitivity with respect to share price changes

df = degree of freedom

dz = random variable exp = Euler value

ESo = Expected Shortfall at issue day Fl

(.) = distribution function of losses

? = gamma, option price sensitivity with respect to delta changes

? = curvature of probability weighting function

H = barrier level

Ho = null hypothesis

Ha = alternative hypothesis

? = risk aversion

? = confidence level

jp = price jump

ja = volatility jump

? = participation factor

L = trading loss

? = loss aversion

m = issuer margin

µ = mean outcome

n = number of time intervals

N(.) = cumulative normal distribution function

N^{1} ?(.) = inverse cumulative distribution function

? = option value

p = prospects

p = objective probability

? = trading profit

p(.) = decision weighting function

p(.) = decision weighting function with time delay

pdf = probability density function

put = put option (European style)

Putui = put option, up-and-in (American style)

putATM = put option, at-the-money (European style)

putoTM = put option, out-of-the money (European style)

putdi = barrier put option, down-and-in (European style)

putdo = barrier put option, down-and-out (European style)

putui = barrier put option, up-and-in (European style)

putuo = barrier put option, up-and-out (European style) q = dividend yield in %

Q = quantile level

Ri = revenue model

r = risk-free interest rate in %

f = scaling factor

s = volatility in %

Oil = volatility (daily) in %

s = survival probability in %

St = share price at any day t

St = share price at maturity T

So = share price at issue day

t = 0

SL = stop loss limit

T = maturity

T = theta, option price sensitivity with respect to time changes

? = utility function

? = unhedged trading position

v= value function

? = vega, option price sensitivity with respect to volatility changes

V(P) = set of risky prospects p

Wt = Geometric Brownian motion

CO = multiplier to measure regulatory value-at-risk amount

w(.) = weighting function

w(.) = true probability weighting function

X = absolute value

XR = reference point

?? = difference = x - XR

Xi = any strike price

X1TM = strike price (in-the-money)

Xatm = strike price (at-the-money)

X0TM = strike price (out-of-the-money)

z = zero coupon bond

? = hazard (mortality) rate

## 1 Introduction

### 1.1 The problem

The market for retail investment products is traditionally dominated by saving deposits, various types of funds, and life insurance products. The liberalization of the capital market in the 1990s and the foundation of option exchanges gave more investors access to derivative products.

Financial institutions started to manufacture investment products as a combination of zero-coupon bonds or shares and derivatives. Structured equity products are "wrapped" into bond-like structures, receive security identification numbers, and are traded on regulated markets. Issuers quote bid and ask prices to make the products available for buying and selling activities.

Investors pay a notional amount upfront in the form of a lump sum and get access to payoff profiles otherwise not offered in the private wealth management market. Financial institutions distribute the structured equity products through their retail advisory channels in which intermediaries give personal advice to retail clients about the attractiveness of products.

The financial market crises in the year 2008 made several poor selling practices evident and revealed the existence of questionable structured equity products in the wealth management of financial institutions.^{1} The lack of strict governance rules in the issuing process of structured equity products became apparent.

Financial institutions were criticized for making structured equity products artificially complex, overpricing products, behing against clients’ risk positions and designing products for implementing a wealth transfer model from retail clients to financial institutions.

The packaging of derivatives and zero-coupon bonds or shares into bond-like products mimics safety and blurs risk perception. The various embedded derivative products remain untraceable for retail investors and widen the information asymmetry between issuers and retail clients. The sub-prime debacle in 2008 demonstrated how financial institutions all around the world have used securitization techniques as tools to remove undesirable assets from their balance sheets. All this qualifies for a moral hazard problem and leaves open suspicion that financial institutions sell equity exposure off their books without identifying target markets and without ensuring that the offered products match the retail clients' desires.

Poor risk disclosure and low transparency spreads mistrust among private households and destabilizes the effectiveness and integrity of the financial market. When financial institutions are not trusted, there is an impact on society's wealth. Banks have a central position in the financial system. Clients could withdraw deposits, and transformation processes slow down and endanger an economy's credit supply.

The study's results should be analyzed by the banking industry to establish product governance arrangements in order to protect households' welfare and bring trust to capital markets. This trust is necessary for developed economies to function.^{2}

### 1.2 Research gaps and objectives

Product manufacturers, such as investment banks, operate on complete capital markets under the assumption of arbitrage-free conditions. Structured products are a combination of zero-coupon bonds or dividend paying shares and a set of over-the- counter (OTC) derivative elements. The products are self-financing.

Interest rates earned from zero-coupon bonds or dividends received from shares are used to finance the embedded options. All components are valued separately under risk-neutral pricing assumptions and the law of one price.

Mainstream research focuses on structured products from a client perspective, see Hens and Rieger (2008, p. 3), Boyle and Tian (2008, p. 303), Rieger (2012, p. 109), Jessen and Jorgensen (2012, p. 7), Chang, Tang, Zhang (2015, p. 598). Only a few studies explore product designs from the issuer’s perspective.

Henderson and Pearson (2007, p. 4) analyzed the u.s. market and observed that products based on stocks have concave payoffs. In contrast, products based on indexes have convex payoff profiles. Henderson and Pearson argued that issuers can offer any payoff profile unless the product is too costly or too difficult to hedge (P-1).

Bernard, Boyle and Tian (2007, p. 25) explored the optimal design from the seller’s perspective. They concluded that issuers are risk-neutral when issuing capital protected products, but have a utility in the outcome when issuing products without capital protection.

Ian Carlin (2009, p. 284) developed a model in which issuers make the design of structured equity products strategically complex in order to escape competition with other issuers. The model assumes that issuers can design products as they wish (p. 282). Celériér and Vallée (2012, p. 27) agree to the findings that complexity is a tool that is used to avoid competition.

Various authors critize the high margin earning possibilities for issuers, see Griinbichler and Wohlwend (2002, p. 22), Wilkens, Emer, Röder (2003, p. 14), Syzmanowska, Horst and Veld (2008, p. 4), Henderson and Pearson (2011, p. 227), Baule and Tallau (2011, p. 54) and Jorgensen, Norholm, Skovmand (2011, p. 25). In contrast, other authors — such as Döhrer, Johanning, Steiner and Völkle (2013, p. 4) and Maringer, Pohl, Vanini (2015, p. 21) — indicated problems with technical procedures for how structured equity products are revalued in previous literature. More clarifications are needed with regard to margin earning possibilities.

There are no studies addressing the budget constraints that issuers have in designing structured equity products. The budget constraints determine launch capabilities, product preferences, and finally maximum margin earning potential.

Financial institutions that issue structured equity products and operate as market- makers in the secondary market take the counterpart of retail order flows. There are reasons to suspect that issuers benefit from the product outcomes and are interested in offloading risks from their trading books to reduce risk exposure in their trading books; see Bergstresser (2008, p. 4), Célérier and Vallée (2012, p. 17). Bernard, Boyle and Tian (2007, p. 1063) noted that issuers of products without capital protection are not risk-neutral and have a utility in the outcome of products.

As of yet, no literature measures the impact of warehousing a client’s counter position in the trading book until maturity. The study shed light on the behavior of issuers at issue day and during structured equity products' lifetimes.

Retail clients are well known for their behavioral-driven investment style. Barberis and Thaler (2003, p. 1063) provided an overview on investors' behavior. Several studies explain the desirability for structured products through behavioral biases.

Shefrin and Statman (1993, p. 124) confirm that the attractiveness of structured products can only be explained through behavioral aspects. Other authors are more specific and conclude that the attractiveness of structured equity products can only be explained by misestimating probability (Rieger, 2012, p. 117) or by clients’ over-optimism and overconfidence (Hens and Rieger, 2014, p. 679). Finally, Döbeli and Vanini (2010, p. 1408) explored that client-friendly communication styles (description in simple words) motivate retail investors to purchase structured equity products.

There are no investigations that attempt to explain what specific design features increase the desirability for structured equity products from the viewpoint of behavioral-driven retail investors. Hens and Rieger (2014, p. 674) wrote: “no comprehensive studies have yet attempted to understand which types of structured products are attractive for private investors and for what motives, although this topic has recently drawn much attention for a number of papers.”

Overall, there is a missing link in literature about whether the manufacturer’s design possibilities can match clients' desire for structured equity products. This link is essential for understanding the benefits of structured equity products for retail clients' wealth accumulation. This link would also help assess whether the design features have the quality to complete capital markets.

The research project contributes in four ways: • to find out the design calculus of product manufacturers for the construction of equity structured products for retail clients in wealth management.

- to determine the root for product complexity and to explore product and maturity preferences of issuers and maximum margin earning possibilities.

- to verify risk-neutrality of issuers at issue day and to ensure that issuers have no interest on the outcome of product at maturity.

- to assess design features that match the client’s desirability for structured equity products in a dynamic market environment.

### 1.3 Structure and methods

The first chapter gives an overview of the various types of structured equity products. The chapter continues with a short introduction of the risk-neutral option pricing theory. The chapter identifies relevant price parameters for the design of products. It also links budget constraints to option pricing models to assess launch possibilities at different interest rates, dividends, and volatility levels.

Linear optimization techniques are used to measure maximum design parameters such as barrier levels, second strike prices, or participation factors under budget constraints. The sensitivity analysis — with respect to time changes — focuses on maximum margin earning possibilities, and issuers' product and maturity preferences.

The purpose of chapter two is to clarify issuers' risk-neutrality. A historical simulation over a period of ten years replicates option price paths of typical option positions that are counterparts of two structured equity products. The simulation is conducted in a trading book environment with position limits, dynamic loss limits, and intraday stop loss limits.

The last chapter applies a modem type of Prospect Theory to measuring retail clients’ utility for structured equity products. Outcomes are weighted by Prelec’s two parameter weighting functions. Time delays are introduced by modifying the weighting function according to Epper and Fehr-Duda (2015, p. 12). Rank dependent utility by Quiggin (1982, p. 329) determines decision weights. Decision weights are implemented in the domain of losses and gains. Utilities are transformed to certainty equivalents. Investors can choose from risk-free assets, shared positions, or structured equity products. The highest certainty equivalent of the three products determines the client’s preference for a certain asset. Certainty equivalents for all asset classes are mapped to µ-s matrixes. The chapters end with short summaries. Final discussions should motivate new research projects.

## 2 Design possibilities of structured equity products

### 2.1 Introduction

One of the most discussed developments in the modem capital market is the increased use of derivatives, such as swaps, futures and options over the last 30 years.

The origin for the success of options was the valuation of option prices through a model described by Fischer Black and Myron Scholes in 1973.^{3} The model and its solutions triggered a boom in option trading around the world. The foundations of futures and option exchanges such as SOFFEX^{4} (1988), Deutsche Terminbörse (1990), OMX^{5} (2003), MATIF^{6} (1987) and LIFFE^{7} (1982) completed the European capital market. This was the first time institutional and retail investors had access to a broad range of options from underlying European stocks and indexes.

During the last two decades, equity options emerged on the retail investment market in a new investment format. Equity options were bundled or wrapped together with zero-coupon bonds or shares and appeared as “bond-like” products. This “packaging” technique allowed many retail investors to have access to equity options that would otherwise not be possible (Wallmeier, 2010, p. 314). The products are listed on regulated markets or alternative trading facilities that have mlebooks and market surveillance standards similar to regulated markets. They are cleared and settled under security identifiers such as ISIN codes and trade with reduced nominal amounts of 100 to give access to a broad class of retail investors.^{8}

Over the years, the knowledge gap between investors and product manufacturers has widened (Lusardi and Mitchell, 2013, p. 6). Financial institutions are criticized for increasing the complexity of products (Carlin, 2009, p. 279), to attract clients with teaser rates, to blur risk perception (Pervenche, 2013, p. 8), to intentionally confuse clients (Célérier and Vallée, 2014, p. 29), to utilize the knowledge gap in order to mislead the likelihood of getting maximum returns (Bernhard, Boyle and Gomall, 2011, p. 78), to escape competition (Célérier and Vallée, 2012, p. 2), to increase search costs (Ellison and Wolitsky, 2009, p. 2) or to charge high margins, see Wilkens (2002, p. 14), Griinbichler and Wolland (2002, p. 22), Szymanowska, Horst, Veld (2008, p. 4), Henderson and Pearson (2011, p. 227), Jorgenson, Norholm, Skovmand (2012, p. 25). The cost to the society is high. The European Systematic Risk Board (2015, p. 6) approximated that the redress costs to clients was more than Euro 100 billion over the last 5-years.^{9}

The chapter contributes to the literature of household finance by exploring the design calculus, product launch possibilities and the motivations of product manufacturers to make the designs of investment products more sophisticated. The chapter also complements pricing literature of structured equity products by giving insights into the maximum margin earning possibilities and product preferences of issuers.

The literature about design preferences of structured products for the retail market from the perspective of issuers is thin. Allen and Gale (1994, p. 252) introduced a model to describe the risk-sharing possibilities of complex products to match the interest of investors. Carlin explained on the basis of a game that issuers increase revenues from uninformed consumers by adding complexity (Carlin, 2009, p. 279). Célérier and Vallée made empirical investigations about product complexity. One of their finding is the positive link between increased complexity and profitability of financial products (p.18). Henderson and Pearson (2007, p. 4) examined patterns in the payoff profile of structured equity products. Products based on indexes offer convex payoffs and products based on individual shares offer concave payoff profiles. Bergstresser (2008, p. 10) detected the issuer’s preferences to launch structured equity products with underlying shares that are easy to hedge.

This chapter presents an analytical method to explore design calculus, product launch possibilities and product preferences of issuers. The root for the complexity of products lies in interest rates, dividends, and volatility levels. Products with budget constraints cannot be randomly designed. To escape budget constraints, issuers modify structured equity products in order to widen their margin earning potential. Product manufacturers have clear product preferences regarding embedded options and maturity. The chapter identifies natural margin ceilings of structured equity products. Finally, it is demonstrated that not only the most complex products are favored by issuer, but also simple products.

The first part of this chapter gives a brief introduction into various categories of structured equity products and what types of options are embedded to design certain payoff profiles. The second part specifies market given constraints responsible for the design of structured equity products and lists design parameters to widen product launch possibilities. The last part explores design preferences of issuers and examines the margin earning potential for issuers.

### 2.2 Overview of structured equity products

The Swiss Structured Products Association (2016)^{10} categorizes structured equity products for the wealth management market in four categories: capital guaranteed products, yield enhancement products, participation and leveraged products. Since leveraged products are standalone warrants, the products cannot be considered to be structured equity products (Bliimke, 2009, p. 33).

The building blocks of structured equity products are either fixed income securities in the form of risk-free zero-coupon bonds or certain units of underlying shares in combination with certain units of equity options (Das, 2001, p. 399). Product manufacturers give issuers design ideas. Issuers package the product and explore launch possibilities in the retail market. Product manufacturers and issuers are often not vertically integrated in one legal entity and have even their place of jurisdiction in different countries. The zero-coupon bond either serves to guarantee the repayment of the notional amount (capital protected products) or serves as collateral for writing options (yield enhancement products). Underlying shares are used to replicate the performance of the equity exposure (participation products). Investors dispense on dividend payments. The notional amount paid upfront finances the zero-coupon bond or the underlying shares and all embedded options. Hence, issuers follow a self-financing strategy.

Structured equity products are traded in the form of certificates on electronic trading platforms. Issuers denominate the volume of the issue amount into smaller redemption amounts, usually in units of 100. From the legal point of view, certificates are unsecured senior liabilities from the issuing financial institution. If an issuer is insolvent, the investor will face the total loss of the notional amount.^{11} The next subchapter gives a brief introduction to the various structured equity products that appear in the retail market in the form of certificates.

#### 2.2.1 Capital protected certificates

Capital guaranteed products ensure that the redemption amount does not fall below the invested capital. The products have a convex payoff. Investors benefit from rising share prices St at maturity T. The loss potential is limited to the amount invested.

In a classical capital protected product investors participate in rising share prices St above a certain strike price Xatm. The payoff at maturity T is

Abbildung in dieser leseprobe nicht enthalten

Products are constructed as a combination of a zero-coupon bond z with a risk-free interest rate r until maturity T. Assuming a notional amount of 100: (2) Z(r,T) = 100 * e?rT

The long at-the-money call options^{12} with share price So = strike price Xatm at issue day t = 0, volatility s, interest rate r, dividend yield q and expiration T guarantee investors to participate in rising share prices: (3) call(S0, XATM,a,r,q,T)

A variety of other capital guaranteed products exists. The products differ in the type and amount of options embedded in the risk-free zero-coupon bond Z(r,T).

Capital protected certificates with a participation factor of ? (0 < ? < 1) embed ? units of call options: ? * call(S0, XATM,a,r,q,T)

At maturity, investors receive the payoff:

Abbildung in dieser leseprobe nicht enthalten

call(S0, XATM,a,r,q,T) - eall(So,X0TM,a,r,q,T)

Both options have the same notional amount and maturity T. At maturity, the investor receives the following payoff with ?0?? > Xatm: Xotm - Xatm; if St > ?0?? St - Xatm; if Xatm < St = Xotm 0; if St = Xatm

Abbildung in dieser leseprobe nicht enthalten

The combination long call and short call with different strike prices curbs the upside potential to the difference Xotm - Xatm.

The last certificate in this category are capital protected certificates with a knock-out trigger at barrier level H, where H > Xatm. The payoff at maturity is given as:

Abbildung in dieser leseprobe nicht enthalten

The type of options embedded at issue day t = 0 are European style up-and-out call options (calluo) with an at-the-money strike price Xatm, where H > Xatm.

(9) calluo(S0,XATM,El,G,r,q,T)

In case the share price St moves up and reaches the barrier level H at any day t with 0 < t < T, the option is knocked-out and ceases to exist. The investors have no claim on the performance St - Xatm.

#### 2.2.2 Yield enhancement certificate

Yield enhancement certificates bear a coupon and are sold as bond-like products. The products have concave payoff profiles. The upside performance is capped. Most of the products are designed without a loss threshold. The notional amount that is paid upfront serves as collateral to compensate for the potential loss exposure of written put options.

The basic investment format builds a reverse convertible certificate. The product is designed as a combination of a zero-coupon bond and a short put option. The option sold at issue day t = 0 is a standard European at-the-money put option.

(10) put(So,XATM,a,r,q,T)

At maturity, investors bear the risk of an assignment. This means that retail investors have to purchase the underlying asset at strike price Xatm. The premium earned reduces losses.

The payoff profile at maturity is:

Abbildung in dieser leseprobe nicht enthalten

The maximum amount an investor can earn is limited to a short put premium (put) and interest rate (r) earned on the collateral amount. The put option premium and interest rate amount is repackaged to a bond-like coupon. Other popular yield enhancement products are protected reverse certificates and barrier reverse certificates.

The protected reverse convertible certificate consists of a long put option (putoTM) with an out-of-the money strike price (????) and a short put option (putATM) with an at-the-money strike price (Xatm)

(12) put0TM(So,X0TM,a,r,q,T),

(13) putATM(So,XATM,a,r,q,T).

Both options have the same notional amount and maturity T. At maturity, the investor receives the payoff:

Abbildung in dieser leseprobe nicht enthalten

Investors receive a coupon as the difference between the short put (putATM) with strike Xatm minus the long put (putoTM) with strike ????, where ???? < Xatm, and interest rate r earned on collaterals.

Finally, barrier reverse convertible certificates. Investors are short a down & in put option (putdi) with an at-the-money strike price (Xatm) and a barrier level H, where H< Xatm.^{13}

(15) putdi(So,XATM,H,G,r,q,T)

When the share price St is below the barrier level H at any day t with 0 < t < T, the short put option knocks-in. If the share price remains below Xatm, investors have to bear the loss of the underlying share price St - Xatm at maturity. The put premium (putdi) and interest rate r reduce the loss. The payoff at maturity is

Abbildung in dieser leseprobe nicht enthalten

#### 2.2.3 Participation certificates

The last group of structured equity products are participation certificates. They offer retail investors an unlimited upside potential but no downside protection. The cash flow paid upfront by investors is used to purchase a dividend paying share.^{14} Dividend payments are used to finance the embedded options. Hence, investors dispense on dividends. The most famous products of this category are airbag certificates, bonus certificates, and outperformance certificates.

Airbag certificates offer clients an unlimited upside potential of a dividend paying share. A downside protection exists between Xatm and certain threshold level X1TM, where X1TM < Xatm. The product consists of a long at-the-money call option with strike price at Xatm and Xatm/Xitm units of a short in-the-money call option with an in-the-money strike price X1TM

(17) call(So,XATM,a,r,q,T)

(18) Xatm/Xitm * call(S0,X1TM,a,r,q,T)

and Xatm/Xitm units of a dividend paying share position (Bliimke, 2009, p. 61).^{15}

Abbildung in dieser leseprobe nicht enthalten

The long at-the-money call option gives investors the possibility of participating in rising share prices. A downside protection exists between the strike prices Xatm - Xitm, which is named “Airbag”. For stock prices St below X1TM, the loss potential is leveraged by the factor Xatm/Xitm. The larger the “Airbag”, the higher the leverage.

With bonus certificates, investors profit from an unlimited upside potential. Between a certain price range Xitm - H, where H < St < Xitm with 0 < t < T, issuers pay a bonus amount. To design bonus certificates, an issuer is long a dividend paying share and long an in-the-money down-and-out put option (putdo) with strike price Xitm > So and barrier level H, where H < So < Xitm.^{16}

(20) putdo(S0,X1TM,H,G,r,q,T)

The bonus level depends on the difference Xitm - So - putdo. The payoff at maturity is:

Abbildung in dieser leseprobe nicht enthalten

Once the share price St touches the barrier level H, investors have lost the bonus and fully participate in the upside or downside of the underlying share price St at maturity.

The last product is an outperformance certificate. Investors benefit from rising share prices at an accelerating rate, but are also exposed to the full downside

Abbildung in dieser leseprobe nicht enthalten

The product is a combination of a dividend paying share and a certain factor ? of a long at-the-money call option (0 < ? < 1):

(23) (1 + ?) * call(So,XATM,a,r,q,T)

The dividend paying share participates investors in the up and down movements of the underlying share price. The at-the-money call option with factor ? provides investors with an outperformance at the rate (1 + k).

The chapter describes structured equity products through payoff functions at maturity. Payoff functions are made visible to clients with profit and loss diagrams and serve as a tool to speed up the learning curve for retail clients.

### 2.3 Design calculus

In complete markets and in a world of perfect information, retail investors could replicate the mentioned pay-offs without financial intermediaries.^{17} However, the elements of the structured equity products are not available in a standardized form in option exchanges.^{18}

Financial intermediaries have the design monopoly on structured equity products. The design possibilities are bound to price operators,^{19} budget constraints, and market conditions. Before a product is released, issuers examine budget constraints and market conditions.

#### 2.3.1 Budget constraints

Structured equity products follow a self-financing strategy. The cost of embedded options are either financed through interest rate proceeds or dividend payments. Budget constraints arise when the cost of embedded options is higher than the interest rate proceeds or higher than dividend payments. For products in which the upfront cash-inflow by retail investors serves as collateral for short-options, there are no budget constraints.

From the perspective of product manufacturers, the products are first grouped in products with and without budget constraints and then according to self-financing strategies, see table 1.

Table 1

Abbildung in dieser leseprobe nicht enthalten

At capital protected certificates are the interest rate proceeds of one unit of a zero coupon bond the budget for the purchase of certain units of options. Issuers can launch capital protected certificates if the interest rate proceeds are sufficient to finance the option premium. To design participation certificates, investors have to dispense on dividend payments. The dividend payments build the budget to finance embedded options. Issuers launch participation products when the dividend income covers the cost of embedded options. The notional amount at yield enhancement products is used as collateral for certain units of short put options. Since the option premium is a cash-inflow, there are no budget constraints.

The next subchapter gives insight into the design possibilities that product manufacturers have to design structured equity products. Interest rate levels r, dividend yields q, and volatility ??are the driving factors for budget constraints. This subchapter shows how product manufacturers solve budget constraints by introducing additional input parameters and how the launch capability of structured equity products has widened across the (G,s), respectively (q,a) space.

#### 2.3.2 Risk-neutral option theory

In the risk-neutral option pricing theory, the stock price change per unit time dSt is a Geometric Brownian motion (Hull 2006, p. 270), which is the solution to the stochastic differential equation: (24) dSt = pStdt + aStdz

Where µ is the expected return and s is the volatility. The Wiener process dz is used to describe the Geometric Brownian motion. Assuming the underlying stock pays a continuous dividend q, the European call option premium, given today’s stock price So, strike price X, volatility s, risk-free rate r, dividend yield q, and maturity T is described as:^{20}

Abbildung in dieser leseprobe nicht enthalten

N(.) is the cumulative normal distribution function. The European call option premium and put option premium could be denoted as

(28) call(So,X,a,r,q,T)

(29) put(So,X,a,r,q,T)

to illustrate the specific dependence of the option premium on the variables.

#### 2.3.3 Base models

The key question in the design process is to find the market parameters determining design possibilities and the conditions under which structured equity products can be issued. The base models use pricing models without hedging costs, issuer margins, and distribution costs.

##### 2.3.3.1 Interest rate proceeds as budget constraints

At issue day pays the retail investor the notional amount to the issuer. The issuer guarantees the full repayment of the notional amount, which is realized by investing the present value of the notional amount in a risk-free zero-coupon bond. The price of one unit of the zero-coupon bond assuming a notional amount of 100 is

(30) Z(r,T) = e?rT

The budget ? per unit, is a function of So, r and T.

(31) B(S,r,T) = So - So * Z(r,T) = So - Soe?rT

In the base model, a capital protected certificate is designed to offer retail clients an asymmetrical (convex) payoff at maturity T through the purchase of an at-the- money call option, which is financed by the budget B. The capital protected certificate can be issued if the interest rate proceeds are sufficient to finance call options. That is,

(32) So - Soe?rT - Soe?qTN(d1) - Xe?rTN(d2) > 0

Since the embedded call option is at-the-money So = X and the time to maturity is assumed to be T = 1, the condition to issue can be further simplified by replacing So for X. Equation (32) changes to:

(33) X - Xe?r - Xe?qN(d1) - Xe?rN(d2) > 0.

After cancelling out X, the condition changes to:

Abbildung in dieser leseprobe nicht enthalten

With S0 = X and T = 1 the formulas for d1 and d2 of equation (26), (27) reduces to

Abbildung in dieser leseprobe nicht enthalten

Putting d1 and d2 in equation 34, the information content is reduced to:

Abbildung in dieser leseprobe nicht enthalten

Only ???? parameters determine the design of capital protected products. This is the interest rate r, dividend q, and volatility s. As long as the interest rate r is higher than the term on the right, the capital protected certificate can be issued (see Appendix A): in the special case r = q, the condition for the last term becomes

(39) r>ln(N(£)_M (_£) + !), or

(40) r>ln(2N(f))

Now the design possibilities only depend on the parameters r and s for a given maturity T = 1. Hence, product manufacturers are bounded in their design possibilities in times of rising volatility and falling interest rates.

##### 2.3.3.2 Dividend proceeds as budget constraints

For participation certificates, the notional amount that a retail investor pays is invested in one unit of underlying shares. Investors dispense on dividend yield q. The issuer’s budget to finance one unit of a certain type of embedded option is limited to the expected dividend income per unit:

(41) B(S,q,T) = So - Soe?qT

In this second base model, a certificate is designed for retail investors to participate in falling or rising share prices. The expected dividend income is used to purchase an at-the-money call option So = Xatm to ensure that retail investors participate in rising share prices at time T = 1. The condition for launching the product is subject to the following budget constraints:

(42) So - Soe?qT - Soe?qTN(d1) - Xe?rTN(d2) > 0.

As before with So = X and T = 1, equation (42) becomes

Abbildung in dieser leseprobe nicht enthalten

After cancelling out X and solving for q, the design possibilities again depend on r, q and s given a maturity T = 1. As long as the dividend q is higher than the term on the right,

Abbildung in dieser leseprobe nicht enthalten

the participation product can be issued, see Appendix B.

Abbildung in dieser leseprobe nicht enthalten

Design possibilities depend on q, s.

#### 2.3.4 Product launch possibilities

The centerpiece in the design process builds an at-the-money option with strike X = So. Strike prices for calls above the share price (X > So) do not allow investors to benefit from the upside performance between X - St. Also strike prices below the share prices (X < St) do not guarantee a full repayment at maturity.

From the full set of input parameters for calls and puts

(47)call(So,X,a,r,q,T)

(48)put(So,X,a,r,q,T) the information content coming from the share price So and strike price Xatm = So is limited. The input parameter s and r are external market parameters and out of the control of product manufacturers. The only parameter that a manufacturer can influence in both base models is the maturity T and the dividend level q, which depends on the choice of underlying assets.

The matrixes below show the launch possibilities of an at-the-money call financed by interest rate proceeds (Figure 1) or financed by dividend income (Figure 2). The matrix allows values for interest rate r or dividend q between 0.5% < r < 6% and values for volatility s between 15% < s < 50%.

If the market conditions between year 2000 and 2016 are mapped into the (G,s) matrix of Figure 1 and (q,a) matrix of Figure 2 it becomes evident that issuers were not able to launch a certificate with an at-the-money call option financed by interest rates or dividend payments at market conditions that prevailed between 2000 and 2016 (see red color).

Abbildung in dieser leseprobe nicht enthalten

Appendix c lists interest rates levels of the 12-month Euribor,^{21} implied volatility levels of a 12-month at-the-money call option and the average dividend yield of the German DAX index between year 2000 and 2016.

Issuers face a dilemma when the costs of standard call and put options exceed the budgets. The design possibilities are bounded in times of rising volatilities (the value of the option rises) and falling interest rates or lower dividend payments (the budget shrinks). Product manufacturers solve this dilemma by introducing:

- participation factors k,

- exotic options with barrier levels H,

- second or third options with strike prices Xi different from Xatm = So.

Issuers can now actively control the level of k, H and Xi. The next subchapter shows products as a combination of zero-coupon bonds, call and put options, barrier options or underlying shares. The chapter demonstrates how the conditions for launching products have improved with the introduction of k, H and Xi.

##### 2.3.4.1 Capital protected certificates

To issue a capital protected certificate, the interest rate budget ? = So - Soe?rT must be high enough to cover the cost of the embedded options. To lower the cost of capital protected certificates, the embedded option structure is modified through the introduction of

- short out-of-the money option with strike ?0??, see equation (49)

- participation factor k, see equation (50)

- long up-and-out call (calluo) with barrier level H, see equation (51).

The decision rules to launch each product depend on the following budget constraints, with ???? > Xatm, ? < ? < 1 and H > Xatm:

(49) So - Soe?rT - call(So,XATM,a,r,q,T) + eall(So,X0TM,a,r,q,T) > 0

(50) So - Soe?rT - ? * call(So,XATM,H,G,r,q,T) > 0

(51) So - Soe?rT - calluo(S0,XATM,H,G,r,q,T) > 0

The matrixes below demonstrate launch capabilities of capital protected certificates. The colored areas in figures 3, 4 and 5 display (G,s) combinations in which the interest rate proceeds exceed the cost of embedded options. Issuers are then in the position to launch the product in the retail market. Dividend levels have an impact on call prices. The colors gray, green and orange indicate various dividend levels q.

Issuers can widen the launch possibilities either through lower out-of-the money short call options with strike ?0?? (see figure 3), lower participation factors ? (see figure 4), or up-and-out call options calino with lower barrier levels H (see figure 5).

Abbildung in dieser leseprobe nicht enthalten

Figure 3. Launch of capital protected certificates with caps.

Left figure with strike price ?0?? = 120, center figure with strike price ?0?? =115, right figure with strike price ?0?? = 110. Each cell contains the interest rate budget ? = So - S1;>e?rT minus the net premium for an at-the-money call option, call(S?.X v1M.o.r.q.T) with So = Xatm =100 and a short out-of-the money call option, call(So,X0TM,a,r,q,T) with ?0?? > Xatm. For both options is T = 1 year.

Color inserts display launch possibilities for various levels of dividend yields q: gray = {q I q = 0% or q = 3% or q = 7%}; green = {q I q = 3% or q = 7%}; orange = {q I q = 7%}; white = {}. Source: Own calculation.

Abbildung in dieser leseprobe nicht enthalten

Figure 4. Launch of capital protected certificates with participation factors.

Left figure with participation factor ? = 0.5, center figure with ? = 0.25 and right figure with factor ? = 0.10. Each cell contains the interest rate budget ? = So - S1;>e?rT minus the premium for an at-the- money call option, ? * call(S?.X vr\1.0.r.q.T) with So = Xatm =100 and T = 1 year.

Color inserts display launch possibilities for various levels of dividend yields q: gray = {q I q = 0% or q = 3% or q = 7%}; green = {q I q = 3% or q = 7%}; orange = {q I q = 7%}; white = {}. Source: Own calculation.

Figure 5. Launch of capital protected certificates knock-out barriers.

Abbildung in dieser leseprobe nicht enthalten

Left figure with barrier level H = 130, center figure with barrier level H = 120 and right figure with barrier level H = 110. Each cell contains the interest rate budget ? = So - S1;>e?rT minus the premium of an up-and-out call option, calluo(S0,XATM,H,a,r,q,T) with So = Xatm =100 and T = 1 year.

Color inserts display launch possibilities for various levels of dividend yields q: gray = {q I q = 0% or q = 3% or q = 7%}; green = {q I q = 3% or q = 7%}; orange = {q I q = 7%}; white = {}. Source: Own calculation.

##### 2.3.4.2 Yield enhancement certificates

The most popular product in this product category is the reverse convertible certificate.^{22} The notional amount paid-in at issue day serves as collateral for written put options. To issue one unit, clients go short a certain unit of at-the-money put option with strike price Xatm = So.

The interest rate budget ? = So - Soe?rT and the premium of the short put option p are wrapped to a bond-like coupon and paid at maturity T = 1, see

- short at-the-money put option in equation (52).

Product manufacturers modify the products through embedding a

- second long out-of-the money put option, see equation (53)

- short down-and-in put option, see equation (54).

Products have no budget constraints and the conditions under which the products can be issued are always fulfilled. For Xatm = So, ?0?? < Xatm, h < So: (52) So - Soe?rT + put(So,XATM,a,r,q,T) > 0

(53) So - Soe?rT + put(So,XATM,a,r,q,T) - put(So,X0TM,a,r,q,T) > 0

(54) So - Soe?rT + putdi(So,XATM,H,G,r,q,T) > 0

Within this product category, the product with the highest premium income gives the widest set of possibilities to design coupons. This is the reverse convertible. Reverse convertibles consist of a short European style at-the-money put option.

##### 2.3.4.3 Participation certificates

For participation certificates, the retail investor is long a dividend paying share and a certain type of options. The issuer’s budget to finance option combinations is limited to the expected dividend income per unit:

(55) ? = So - Soe?qT

The embedded options are not financed through interest rate proceeds So - Soe?rT, but through dividend payments So - Soe?qT.

Product manufacturers widen their design possibilities through the introduction of a

- participation factor k, see equation (56)

- down-and-out put option, see equation (57)

- second strike price X1TM, see equation (58).

The budget to design participation certificates depends for all products on the dividend yield level q. For ? < ? < 1, H<S0< Xitm:

(56) So - Soe?qT - k* call(S0,XA1M,G,r,q,T) > 0

(57) So - Soe?qT - putdo(S0,X1TM,H,G,r,q,T) > 0

For a notional amount of 100 and with X1TM < Xatm:

Abbildung in dieser leseprobe nicht enthalten

The colored areas in figure 6, 7 and 8 display (q,a) combinations in which the dividend proceeds exceed the cost of embedded options. Issuers are then in the position to launch the product in the retail market. Interest rate levels have an impact on option prices. The colored inserts indicate various interest rate levels r.

The basic product in this category is the outperformance certificate (see equation 56). To design an outperformance certificate, the notional amount is used to purchase one unit of dividend paying shares. The dividend income is used to finance ? units of an at-the-money call option, where ? < ? < 1.

Investors are long one unit of shares and ? units of the at-the-money call. The embedded option guarantees investors an outperformance of (1 + k) at rising share prices. To issue an outperformance certificate, the dividend income must be high enough to finance ? units of the at-the-money call. Issuers have now a set of parameters to influence the launch of this product in the market. They can control the level ? (participation factor) and the level of q (dividend yield) through stock selection. A lower level of ? and a higher level of q increases the possibility of launching outperformance certificates (see figure 6). Interest rate levels have an impact on call prices. The color inserts indicate various interest rate levels r.

Abbildung in dieser leseprobe nicht enthalten

Left figure with participation factor ? = 0.50, center figure with participation factor ? = 0.25 and right figure with participation factor ? = 0.10. Each cell contains the dividend budget ? = So - S1;>e?qT minus the premium for a call option, ? * call(S?.X vr\1.0.r.q.T) with So = Xatm =100 and T = 1 year.

Color inserts display launch possibilities for various levels of interest rates r: orange = {? I ? = 0% or r = 3% or r = 7%}; green = {? I r = 0% or r = 3%}; gray = {? I r = 0%}; white = {}. Source: Own calculation.

**[...]**

^{1} European Commission (2011). Consumer Market Study on Advice within the Area of Retail Investment Services - Final Report, p. 11. According to this study 57 percent of sales across the European Union were classified as "unsuitable" in terms of investment liquidity and risk levels.

^{2} Edelman Trust Barometer (2014). A survey of 27 countries revealed that the banking and financial services industries are the least trusted sectors.

^{3} Black F., Scholes M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, Voi. 81, N0.3, pp. 637-654.

^{4} Swiss Options and Financial Futures Exchange (today Eurex, Frankfurt).

^{5} Optionsmäklama Exchange, in Stockholm and Helsinki (today Nasdaq OMX exchange).

^{6} Marché à Terme International de France (today Euronext, Paris).

^{7} London International Financial Futures and Options Exchange (today, ICE Group, Atlanta).

^{8} Market volume for, e.g. Switzerland around CHF 235 billion in year 2015 according to the Swiss Structured Products Association. In Germany the volume is at Euro 68.6 billion in year 2015 according to Deutscher Derivate Verband.

^{9} Cases of misselling: In Joint Committee of the European Supervisory Authorities (2013), Joint Position of the European Supervisory Authorities on Manufacturers’ Product Oversight & Governance Processes, p. 6.

^{10} Swiss Structured Products Association (2016), SSPA Swiss Derivative Map 2016.

^{11} FSB (2014). Principles of Loss-absorbing and Recapitalisation Capacity of G-SIBs in Resolution.

Principle 10. Notes with derivative features are not eligible as bail-in tools in a bank resolution.

^{12} At-the-money call options with Xatm = So are embedded. In contrast to out-of-the-money call options with X0TM > Xatm, with at-the-money call options investors participate directly in the performance of underlying shares for all share prices higher than the at-the-money strike price at maturity (St> Xatm). In-the-money call options with So > X1TM as an alternative to at-the-money options would increase the cost of launching the product and do not provide an extra performance at maturity T.

^{13} Goldman Sachs (2016), Zertifikate-Kompass, p.33.

^{14} Common practice is the purchase zero-strike call options instead of long share positions. For zero-strike call options, the expected dividend payments are locked-in in the form of a discount S(0)-S(0)e־qT. Issuers do not have to wait until dividend payment dates to receive dividend payments.

^{15} Goldman Sachs (2016), Zertifikate-Kompass, page 53.

^{16} See Goldman Sachs (2016), Zertifikate-Kompass, p. 22.

^{17} MİFID, Article 24,11 requires from issuers to tell retail clients if components can be purchased separately.

^{18} A short put option could be replicated by a long stock position and a short call option position. It is challenging to replicate options with discontinuities in the payoff, such as barrier options. Even professional traders have to approximate hedge positions, because there are no adequate products in the market to replicate barrier options.

^{19} Option price formulas (e.g. American style option price formulas or European style option price formulas).

^{20} Investors of structured equity products have no exercise rights.

^{21} European interbank offered rate.

^{22} In Germany, Switzerland, Austria known as ״Aktienanleihe“.

- Quote paper
- Stefan Modrow (Author), 2017, Involving the Question of Utility for the Design of Structured Equity Products in the Wealth Management Market, Munich, GRIN Verlag, https://www.grin.com/document/441101

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