28.3.1 Structured Products with No Exotic Options

Exhibit 28.1a is representative of a structured product that does not have exotic option features. The payout in Exhibit 28.1a is a simple example of a popular investment known as a principal-protected structured product. A principal-protected structured product is an investment that is engineered to provide a minimum payout guaranteed by the product's issuer (counterparty). For example, a major bank may offer a structured product with a term of five years that has a payout that increases if an underlying index increases but also a minimum guaranteed payout regardless of any declines in the underlying index. Of course, the payout is subject to the counterparty risk of the issuer. Thus, in the context of structured products, principal protection is the promise by the issuer to guarantee the return of most or all of the investor's principal.

Another important feature of many structured products is the participation rate. The participation rate indicates the ratio of the product's payout to the value of the underlying asset. A structured product with a participation rate of 100% has a payout that increases by the same percentage that the underlying asset's value increases. A participation rate of 50% indicates half the risk exposure, whereas a participation rate above 100% indicates leveraged exposure of the structured product to the value of the underlying asset.

Note that principal protection and participation rates are not exotic option features. Simple call options and put options can easily be combined to provide principal protection (e.g., long a put option) and participation rates not equal to 100% (e.g., having option exposures with notional amounts above or below the principal amount of the structured product).

The diagram in Exhibit 28.1a can be constructed with a long exposure to an underlying asset and a protective put. The structured product in Exhibit 28.1a is easy to understand and easy to value, since valuation of simple options is quite easy.

The exposure illustrated in Exhibit 28.1a can also be viewed as a cash-and-call strategy. A cash-and-call strategy is a long position in cash, or a zero-coupon bond, combined with a long position in a call option. The identity between a protective put strategy and a cash-and-call strategy is a straightforward implication of put-call parity, as discussed in Chapter 6. Thus, prices of the components of a structured product may often be related based on the put-call parity relationship.

The structured product depicted in Exhibit 28.1a may be viewed and valued quite simply using simple options. However, the payoffs in Exhibits 28.1b and 28.1c contain exotic options, some of which may be very difficult to price.

28.3.2 Structured Products and Asian Options

Some options have payoffs that depend on market values at multiple points in time. An Asian option is an option with a payoff that depends on the average price of an underlying asset through time.

Consider an Asian call option on oil prices that pays the greater of X – K or zero, where X is the average market price of the underlying asset observed monthly over a one-year period, and K is the strike price. A firm that uses oil every month can purchase this single option and, in so doing, can cap its average oil costs over the 12 months. The purchase of one Asian option is less expensive than the purchase of 12 monthly European options because it offers less protection. However, the protection offered by the Asian option might better fit the firm's desire to lock in a maximum average annual price of the oil purchases.

A path-dependent option is any option with a payoff that depends on the value of the underlying asset at points prior to the option's expiration date. An American option is a path-dependent option because the payoff from the option writer to the option holder can be affected by the values of the underlying asset prior to the option's expiration.

There are other options, discussed in later sections as path-dependent options, that are more complex than Asian options. Note that just because an option has an average price as an underlier does not necessarily mean that the option should be characterized as an Asian option. The averaging process in an Asian option should be based on averaging prices through time. An option on the average price of two or more underlying assets at the same point in time does not typically qualify as an Asian option. For example, on option on the average (non-annualized) return of 10 securities is not an Asian option; it is an option on a portfolio.

28.3.3 Structured Products and Binary Options

Binary options were introduced in Chapter 26 in the context of credit derivatives. In the case of credit options, a binary option provides two payoffs, contingent on whether a specified credit event occurs at any point in time over the life of the option.

The binary options in the structured products in this chapter are European options and are a little different. A binary option in a structured product has two potential payoffs, based on whether the value of the underlying asset is above or below the binary option's strike price at the option's expiration (i.e., at the termination of the structured product).

Exhibit 28.1b illustrates the upward jump in the payoff of a binary call option that occurs when the underlying asset's price exceeds the call option's strike price at the termination of the product. The diagram is discontinuous and is based solely on the final price of the underlier, as illustrated in Exhibit 28.1b. The discontinuous jump in the option price relative to the price of the underlying asset at termination of the product is the key feature of a binary option. Other types of structured products or options, discussed later, offer large price jumps, but they do so either with multiple payoff levels or based on prices other than the price of the underlier at the termination of the product.

28.3.4 Structured Products and Barrier Options

Barrier options are a type of path-dependent option. Structured products often include barrier options. A barrier option is an option in which a change in the payoff is triggered if the underlying asset reaches a prespecified level during a prespecified time period. For example, a structured product that permanently loses principal protection if the underlying asset reaches a specified loss level contains a barrier option.

Barrier option features are either knock-in options or knock-out options. A knock-in option is an option that becomes active if and only if the underlying asset reaches a prespecified barrier. An active option in a barrier option is an option for which the underlying asset has reached the barrier. Once a barrier option has become an active option, the option can affect the payoff without further need for the underlying asset to reach the barrier again. If the underlying asset price never reaches the barrier, then the option remains inactive and expires worthless. Knock-in options can be calls or puts, depending on whether it is a call or put that becomes active.

For example, consider a knock-in call option on an asset with a current price of $100 and a barrier of $110. If the underlying asset moves up and reaches the barrier ($110), the option becomes a simple active call option. Further suppose that the option's strike price is $105. If the price of the underlying asset never reaches the barrier ($110), the option expires worthless. Thus, even if the underlying asset reaches $109 prior to expiration, the option holder receives no payoff if the $110 level was never reached. Once the barrier has been reached, the option will behave like a simple option with a payoff that is determined solely by the relationship between the price of the underlying asset and the strike price.

28.3.5 Characteristics of In versus Out and Up versus Down Barrier Options

The option described in the preceding section is a type of knock-in option known as an up-and-in call option. It is an “up” option because the price of the underlying asset is less than the barrier price at inception, and therefore the underlying asset must move up in price for the option to have value. It is an “in” option because the option becomes active if the barrier is reached. It is a call option because the option that can become active is a call option.

A knock-out option is an option that becomes inactive (i.e., terminates) if and only if the underlying asset reaches a prespecified barrier. If the underlying asset price never reaches the barrier, then the option remains active and can be exercised at expiration. Knock-out options can be calls or puts and be issued as up or down options.

Exhibit 28.2 depicts eight types of options differentiated by being up/down, in/out, or call/put. The up-and-in call option is depicted in the upper left corner.

In the lower right corner of Exhibit 28.2 is a type of knock-out option known as a down-and-out put. A down-and-out put becomes inactive if the price of the underlying asset falls to the barrier. Thus, the payoff of the put is limited to the excess of the strike price (K) above the barrier (H). It is a “down” option because the price of the underlying asset is greater than the barrier price at inception, and therefore the underlying asset must move down in price to reach the barrier. It is an “out” option because the option becomes inactive if the barrier is reached. It is a put option because the option that can become inactive is a put option.

Note that a down-and-out put is not the same as a simple put option spread that is long a put at K and short a put at H (with K > H). The reason is that at expiration, the put spread will pay the greater of K – H or zero. However, the down-and-out put will pay K – H only if the barrier is never reached. If the barrier is reached at any time prior to expiration of the knock-out feature, the barrier put pays nothing.

Note that barrier options should always have values equal to or less than simple options of the same maturity and strike price, as barrier options can have the potential for an earlier expiration and lower payoff.

Exhibit 28.1c illustrates the payoff diagram of a barrier option. Notice that the payoff is no longer purely a function of the value of the underlier at option expiration. Over some of the range, the payoff to the option can take on one of two values depending on the path that the underlier took. Specifically, one path is based on the underlier not having reached the barrier, and the other is based on the underlier having reached the barrier.

Structured products with path-dependent options tend to have complex payout diagrams that capture the paths through multiple payout lines based on conditions related to the paths, as shown in Exhibit 28.1c.

28.3.6 Structured Products and Spread Options

A spread option has a payoff that depends on the difference between two prices or two rates. The option's payoff depends on the difference between the spread at the option's expiration relative to the option's strike price (or strike rate). (Note: A spread option should not be confused with option spreads, discussed in Chapter 6, which are portfolios with multiple call or put positions.)

Consider, for example, a one-year European spread call option with a strike price (or strike rate) of 2% on the difference of the percentage return of a large-cap equity index over the percentage return of a small-cap equity index. Assume that at the end of the year, the large-cap index has risen 10%, and the small-cap index has risen 4%. Accordingly, the spread between the returns is +6%. A spread call with a strike price of 2% would pay 4% (of the option's notional value) to its holder. A call spread option pays its holder when the spread exceeds the strike, whereas a put spread option pays its holder when the spread is less than the strike. A spread put with a strike price of 2% in this example would expire worthless.

Note that the spread between two assets may be represented as either asset #1 minus asset #2 or the reverse, asset #2 minus asset #1. A call spread with a strike of K is identical to a put spread with a strike of –K if the definition of the spread on the put is the reverse of the definition of the spread on the call.

28.3.7 Structured Products and Look-Back Options

Another type of path-dependent option is a look-back option. A look-back option, introduced in Chapter 9, has a payoff based on a minimum or maximum price that occurs over a specified period of time (the look-back period). Typically, the look-back period is the entire life of the option. An in-the-money look-back call pays the maximum price over the look-back period minus the strike price. An in-the-money look-back put pays the strike price minus the minimum price over the look-back period.

28.3.8 Quantos and Other Structured Products

The spectrum of structured products provided by issuers throughout the world to meet investor preferences is astounding. An example of a very specialized option is a quanto. A quanto option is an option with a payoff based in one currency using the numerical value of the underlying asset expressed in a different currency. For example, the Nikkei 225 is a yen-based index of Japanese stock prices. Consider a U.S. dollar–based quanto call option on the Nikkei with a strike price of 17,000 issued when the Nikkei 225 was at 16,000 yen. This quanto call option on the Nikkei 225 would pay $1 for every yen by which the Nikkei 225 exceeded 17,000 yen at the option's expiration.

The preceding discussions have covered some of the major categories of exotic options used in structured products, but other option-driven products exist. For example, some advanced structured products have payouts that depend on the prices of a set of underlying assets. The payouts to these structured products can involve valuations at a variety of points in time (e.g., quarterly over the product's life), resulting in payouts related to some of the underlying asset values being capped or frozen at each valuation point, and payouts related to the remaining underlying assets being allowed to continue to vary until the option's expiration.

28.4.1 A U.S.-Based Structured Product with Multiple Kinks

This product is a hypothetical example based on some of the properties of a product offered by MetLife, a major U.S. insurance company. The product has an annuity wrapper from an insurance company. An investor can choose an underlying asset from a set of indices, including a broad U.S. equity index, a small-cap index, an international equity index, and a commodity index. The investor also selects a maturity term of one, three, or six years. The payout to the contract depends on the performance of the index over the contract term. The distinguishing feature of the structuring is that the payout diagram has kinks at up to three price levels, based on a cap and a floor that can be selected by the investor from a set of available values. A kink may be viewed as the location in a payoff diagram where the slope changes.

The investor may be viewed as first selecting a partial floor of x%. The floor is termed here as “partial” because the issuer covers only the first x% of losses if the index experiences a decline at the end of the term. For losses beyond x%, the investor is at risk (unless the investor selects x% = 100% protection). Thus, if x% = 10%, the investor breaks even if the index has losses smaller than 10%. If the index declines by more than 10%, say 35%, the investor loses the excess of the losses beyond 10% (in this instance, 25%).

Based on the investor's other choices and market conditions, the issuer will impose a cap on profits. For example, a product on the S&P 500 index with a partial loss floor of 10% and a term of three years might offer a cap of 20%. The cap determines the maximum possible payout. Suppose that at the end of the three-year term, the S&P 500 has experienced a capital gain or loss of r%. Here is the payout of the hypothetical product with a partial loss floor of 10% and a cap of 20%:

The product offers investors an ability to tailor their investment as a trade-off between loss protection (the partial floor) and limited profit potential (the cap). The product can be replicated in theory with European options, and therefore, despite its complexity, it does not contain exotic options:

By placing this product in an insurance wrapper, U.S. residents are able to enjoy tax deferral of any gains until the investor receives distributions from the insurance plan.

28.4.2 A French-Based Structured Product with Floors

BNP Paribas, a major global bank headquartered in France, offers a wide spectrum of creative and potentially complex structured products. This description is a hypothetical example based on some of the properties of a product called a Magic Asian with an example term of five years. The payout to the product is based on an average of the percentage gains and losses of a basket of 20 underlying shares. At the end of the term, the average performance of the shares determines the payout to the product except that the product offers a floor return of 20% to the return of every underlying share that returns more than 0%.

For example, assume that the 20 underlying shares experience performance that is evenly spaced in 4% intervals from –18% to + 58% (i.e., –18%, –14%, –10%, … , +54%, +58%). The returns of the five shares losing money and the 10 shares earning more than 20% would be unaltered. However, the returns of the five shares gaining between 0% and 20% (2%, 6%, 10%, 14%, and 18%) would be bumped up to a floor value of 20%.

The product offers a one-year fixed coupon and an attractive floor to shares that gain. The gain to the investor of having floor values can be offset by other factors, such as a low coupon rate. Despite having a payout based on an average of returns, the product would not be properly described as an Asian option because the averaging process does not consider different observation dates. This hypothetical product is a position in a portfolio with floor features that can be replicated with collar option positions:

28.4.3 A German-Based Structured Product with Leverage

The product discussed in this section is a hypothetical example based on some of the properties of a similar product offered in Germany. According to Deutsche Bank Research, certificates are wrappers that offer low trading costs, liquidity, versatile structures, and permanent bid and offer quotes by issuers.¹

The spectrum of products offered in Germany rivals those of other jurisdictions. As an example, a Sprint product combines a long position in an underlying asset with a long call option position at a relatively low strike price that provides upside leverage (e.g., a double participation rate of 200%). The product's double upside protection is capped via short call positions at a relatively high strike price. The result is a somewhat collar-like payoff diagram that offers leveraged participation over a prespecified range but with limited profit potential at very high values:

By placing this product in a certificate wrapper, investors may be able to enjoy a substantial degree of liquidity and low trading costs.

28.4.4 Absolute Return Structured Products in the United Kingdom

The product discussed in this section is a hypothetical example based on some of the properties of a similar product in the form of a zero-coupon note offered by the Royal Bank of Scotland that matured in 2009. The actual product's payouts were based on the performance of the iShares MSCI Emerging Markets Index Fund.

A popular class of structured products offers payouts based on absolute returns. An absolute return structured product offers payouts over some or all underlying asset returns that are equal to the absolute value of the underlying asset's returns. Thus, whether the underlier rises 2% or declines 2%, the structured product pays +2%.

The core concept of an absolute return structured product is easily replicated in the options market with an at-the-money straddle (see Chapter 6). In the case of a long option straddle, the option buyer pays a price or premium to establish the straddle, makes money if the underlying asset makes a large directional move, and loses money if the underlying asset does not move substantially. In the case of a structured product based on absolute returns, the benefit to the investor of gaining from large moves in either direction must be offset by features that benefit the issuer.

A principal protected absolute return barrier note offers to pay absolute returns to the investor if the underlying asset stays within both an upper barrier and a lower barrier over the life of the product. If the underlying asset reaches either barrier, the payout is equal to the principal of the product. Note that as a path-dependent option, the underlying asset may lie inside the barriers at the termination of the structured product but fail to produce absolute returns if its path reached a barrier.

If the barriers are placed 5% from the initial value of the underlier, the principal protected absolute return barrier note would pay the absolute return of the underlier if the barrier was not reached, or 0% if the barrier was reached. This structured product can be replicated as a long straddle position in exotic options (knock-out options):

By placing this product into an individual savings account, many UK investors can enjoy tax-free distributions of any profits.

28.4.5 A Swiss-Based Structured Product Based on Absolute Returns

This product is a hypothetical example based on some of the properties of a similar product offered by Credit Suisse, briefly described as a Twin-Win certificate in its Structured Products brochure.

A structured product can be engineered to offer absolute returns that are more complex than the principal protected absolute return barrier note described in the previous example. Some absolute return products expose the investor to substantial downside risk to offset the cost of providing absolute returns. Consider an absolute return product without principal protection that offers unlimited upside return potential but somewhat complex downside return potential. Specifically, if the underlier does not decline x% or more at any time over the life of the product, the note delivers the underlier's absolute return. However, if the barrier of –x% is reached, the note delivers the actual return of the underlier.

The note, therefore, is equivalent to owning the underlying asset (ignoring any lost dividends) with a down-and-out put (i.e., a knock-out put with an at-the-money strike price):

The investor is fully exposed to large up and down movements in the underlier through the first and final positions in the equation. However, based on the middle position in the equation, if the underlier does not fall to the barrier at any time over the product's life, the investor can receive the underlier's absolute return. Thus, from 0% to –x%, the investor can receive principal protection if the barrier has not been reached.

Investors may be able to use structured products and wrappers to maximize the portion of a return that is attributable to capital gains. This strategy can enhance after-tax total returns to investors located in countries such as Switzerland where there can be tax advantages to receiving investment returns in the form of capital gains rather than income.

28.4.6 A Japan-Based Structured Product Based on Multiple Currencies

Japan's Nomura Securities is part of the Nomura Group, which includes world-class investment and banking activities. Major world financial services firms, including Nomura Securities, offer structured products based on foreign exchange rates and interest rate differentials between currencies.

Consider a power reverse dual-currency note. At its core, in a power reverse dual-currency note (PRDC), an investor pays a fixed interest rate in one currency in exchange for receiving a payment based on a fixed interest rate in another currency. However, the payment that the investor receives is increased or decreased proportionately as the exchange rate between the two currencies changes. For example, if the exchange rate during the life of the note rises to 1.25 from an exchange rate of 1.00 at the inception of the note, the cash payments received by the investor will be changed by the same proportion (25%). Typically, the deal includes various option features, such as caps and floors. For example, the issuer may structure the deal so that any net cash flow of payments from the investor to the issuer is limited.

From the perspective of the investor, the structured product allows for a leveraged carry trade in which the investor attempts to benefit from receiving higher coupon payments than the investor is paying. The product would therefore be attractive to an observer of interest rate differentials between nations who believes they will persist and thus generate benefits that will not be offset by changes in exchange rates.

28.4.7 Liquid Structured Products

Many structured products are listed and are therefore liquid alternatives. For example, in the United States, there are numerous structured products issued by major institutions that trade on the New York Stock Exchange.

A disadvantage of a liquid structured product is that it must be standardized in terms of maturity, participation rates, principal protection, and so forth, in order to attract numerous investors; however, some investors may prefer a structured product that is tailored to their individual preferences. The advantage of a liquid structured product to an investor is not only that the product can be sold through the listing market but also that its price and its price volatility can be observed through time.

Interestingly, although many structured products in the United States continue to be registered with the SEC, the proportion of these products actually being listed has diminished in recent years. Apparently the benefits of listing are not perceived as being worth the costs, yet the products are standardized and registered so that they can be marketed to a wider audience.

28.5.1 Pricing Structured Products with PDEs

Structured products are often valued using the partial differential equation approach. The partial differential equation approach (PDE approach) finds the value to a financial derivative based on the assumption that the underlying asset follows a specified stochastic process and that a hedged portfolio can be constructed using a combination of the derivative and its underlying asset(s).

As a very simplified illustration, consider a riskless security in a world of fixed and certain interest rates. The riskless security is a zero-coupon bond that pays $F at time T. The first step is to express the change in the value of the riskless security. Since it is riskless, the change in price would be equal to the value of the security (P) times the periodic interest rate, which can be factored to produce the following ordinary differential equation:

The fact that the value of the bond must be $F at time T is a boundary condition. A boundary condition of a derivative is a known relationship regarding the value of that derivative at some future point in time that can be used to generate a solution to the derivative's current price. The boundary condition combined with the mathematics of ordinary differential equations generates the following solution to the price of the bond, P, at time t:

In a similar fashion, the PDE approach uses one or more boundary values and a differential equation to generate a price model. There are two major differences between the PDE approach and the previous simple example: (1) The PDE approach uses partial differential equations that are based on two factors, time and uncertainty; and (2) the PDE approach requires construction of a riskless portfolio. Note that in the simplified example, the bond itself was riskless, and hence there was no need to construct a riskless hedge.

Partial differential equations are based on continuous-time mathematics. By specifying the relationship between the changes in two or more variables through time, one can derive a functional relationship between their levels. The PDE approach (1) relates the stochastic process followed by an option to the process followed by its underlying asset, (2) constructs a riskless portfolio by combining the derivative and its underlying asset, and (3) solves for the price of the derivative by setting the return of the riskless portfolio to r and imposing boundary conditions.²

In the case of a simple European option, Black and Scholes derived an analytic solution in the form of the well-known Black-Scholes option pricing model, in which the option price is a simple function of five underlying variables. The boundary conditions are that the call price is zero when S (the price of the underlying stock) is zero; the call price approaches infinity as S approaches infinity; and the value of the call option at expiration is max{S – K,0}, where K is the strike price. The solution is analytical because the model can be exactly solved using a finite set of common mathematical operations. In the case of the Black-Scholes option pricing model, the solution is analytical because the option's price is a relatively simple function of five underlying variables.

Complex options and complex structured products often lack an analytical solution. Cases involving complex underlying stochastic processes or numerous boundary conditions often require solutions through numerical methods. Numerical methods for derivative pricing are potentially complex sets of procedures to approximate derivative values when analytical solutions are unavailable. Numerical methods can be difficult. Solutions to derivative values are often estimated using the methods discussed in the following two sections: simulation and building blocks.

28.5.2 Pricing Structured Products with Simulation

A powerful and popular approach to valuing complex financial positions is Monte Carlo simulation, introduced and discussed in Chapter 5. Consider a complex structured product with possible payouts that depend on the values of two or more underlying assets at various points in time through the product's life.

A solution to the price of such a complex product using the PDE approach may be intractable. However, it is relatively easy to estimate the product's price if the potential paths of the underlying assets can be reasonably estimated.

As a simplified example, a very large number of projected paths for the price of an asset could be formed under the assumption that the price followed a particular stochastic process. The payoffs of a derivative on that asset could then be projected for each path. The discounted values of the derivative payoffs for each path could then be averaged to form an estimate of the current price for the derivative. The simulation approach can be a conceptually simple method of estimating the value of complex derivatives and complex structured products when analytical solutions are unavailable and numerical methods are complex.

28.5.3 Pricing Structured Products with Building Blocks

The building blocks approach (i.e., portfolio approach) models a structured product or other derivative by replicating the investment as the sum of two or more simplified assets, such as underlying cash-market securities and simple options. The value of the structured product is simply the sum of the values of its building blocks. The value of each building block is in turn estimated through observation of market prices or well-known derivative pricing equations (e.g., option pricing models).

The primary distinction between the building blocks approach and the PDE approach is that the PDE approach is based on dynamic hedging. Dynamic hedging is when the portfolio weights must be altered through time to maintain a desired risk exposure, such as zero risk. An example of a dynamically hedged portfolio is a long position in a stock that is initially hedged by a short position in four call options on that stock when the delta of the call option is 0.25. As the delta of the call option continuously changes through time, the number of short calls must be continuously changed to maintain the hedge. Thus, if the delta fell to 0.20 or rose to 0.50, the option hedge would be adjusted to being short five calls or two calls, respectively.

In the building blocks approach, portfolios are formed using a static hedge. A static hedge is when the positions in the portfolio do not need to be adjusted through time in response to stochastic price changes to maintain a hedge. For example, a static hedge approach can be used to value a European put option using a portfolio of three assets: the underlying asset, a European call option with the same maturity and strike price as the put that is being valued, and a riskless bond. As indicated in previous chapters, put-call parity establishes that a short position in the stock, a long position in the call option, and a long position in a riskless bond will replicate the return from holding the put option. Note that the key to the building block approach is that the value of the portfolio at some horizon point (e.g., expiration of the options) will be equal to the value of the derivative that is being valued regardless of what happens to the values of the securities used to create the static hedge.

In practice, the building block positions necessary to replicate a complex structured product perfectly may not be available or may not be trading at informationally efficient values.

28.5.4 Two Principles from Payoff Diagram Shapes and Levels

Exhibit 28.1 illustrates a few of the many different payoff shapes that structured products offer. The payoff diagram shape indicates the risk exposure of a product relative to an underlier. The shape of the payoff diagram can be analyzed by investors to ascertain the extent to which the product's payoffs align with the investor's risk preferences or the investor's market view of the return distribution of the underlying asset.

Exhibit 28.1 does not indicate the level of the payoff diagram relative to the cost of the product.³ The payoff diagram level determines the amount of money or the percentage return that an investor can anticipate in exchange for paying the price of the product. Thus, the investor can use the level of the payoff diagram relative to the cost of the product to estimate whether the product is attractively or unattractively priced.

Principle 1 is that any payoff diagram shape can be constructed given a sufficient availability of options. In other words, any relationship between a portfolio of options and a related asset can be engineered if there are sufficient derivatives with which to manage the exposure. Slopes can be mimicked using calls and puts; discontinuous jumps can be mimicked using binary options.

Principle 2 is that it is the level of the payoff diagram that dictates whether the product is overpriced, underpriced, or appropriately priced. In other words, the vertical level of the payoff diagram drives the relative magnitudes of the profits and losses; therefore, it is the level of the payoffs that determines the attractiveness of an exposure in terms of prospective returns.

The enormous spectrum of structured products available enables investors to locate products that best meet their preferences regarding risk. If an investor's market view turns out to be correct, then the variety of structured products serves the purpose of enabling the investor to better achieve attractive returns or other financial goals.

However, the enormous spectrum of structured products available can also play into the investor's behavioral biases. In other words, an investor analyzing a very large number of diverse structured products may substantially overestimate the value of some products and underestimate the value of other products. The spectrum of available products may lead an investor with behavioral biases into taking otherwise undesirable risks if the investor falsely believes that a particular product is underpriced. For example, investors subject to the behavioral trait known as an overconfidence bias will tend to overweight structured products that appear underpriced based on the investor's market view even when those products are overpriced due to high fees. An overconfidence bias is a tendency to overestimate the true accuracy of one's beliefs and predictions.

28.5.5 Evidence on Structured Product Prices

A key issue in complex structured products is whether the prices at which the investments are issued are fair. In other words, how do the actual prices of the products compare with the estimated prices of the products using market-based valuation methods? The high degree of complexity in some structured products makes valuation challenging and subject to discretion.

Deng and others examine the issue price of principal protected absolute return barrier notes (ARBNs) and find that the fair price of ARBNs “is approximately 4.5% below the actual issue price on average.”⁴

A white paper by McCann and Luo estimates that “between 15% and 20% of the premium paid by investors in equity-linked annuities is a transfer of wealth from unsophisticated investors to insurance companies and their sales forces.”⁵

Some industry sources point to lower fees for some products than those indicated by the previously cited empirical analyses of particular products. For example, in the Bank of Scotland's A Guide to Structured Products, the “total fees & expenses” component (i.e., building block) of its structured products is listed as representing 2% to 3% of the product's price.⁶