### Exotic Options

After completing this reading, you should be able to:

• Define and contrast exotic derivatives and plain vanilla derivatives.
• Describe some of the factors that drive the development of exotic products.
• Explain how any derivative can be converted into a zero-cost product.
• Describe how standard American options can be transformed into nonstandard American options.
• Identify and describe the characteristics and payoff structure of the following exotic options: gap, forward start, compound, chooser, barrier, binary, lookback, shout, and Asian, exchange, rainbow, and basket options.
• Describe and contrast volatility and variance swaps.
• Explain the basic premise of static option replication and how it can be applied to hedging exotic options.

## Exotic Derivatives vs. Plain Vanilla Derivatives

Plain vanilla derivatives represent the most basic version of financial derivatives, including futures contracts, forwards, swaps, and over-the-counter (OTC) instruments used in fairly liquid markets. They have a simple expiration date, exercise price and have no additional features. Exotic derivatives alter the traditional characteristics to create a complex financial instrument that’s tailored to meet the specifications of a particular counterparty.

In plain vanilla derivatives, most details are precisely outlined and straightforward. Such details include the initial cost, current market value, expiration date, amounts to be paid, and the cost of the existing position. For exotic derivatives, most of these issues are negotiable.

Some of the reasons behind the development of exotic derivatives include the need to:

• Create a customized hedge that reflects the composition of an entity’s underlying assets
• Address tax and regulatory concerns
• Develop products that reflect the direction of future market prices

## Conversion of derivatives into a zero-cost product

When two or more derivatives with contrasting features are combined, a package is formed. Common packages include a bull, bear, calendar spread, or even a straddle. Through these packages, a trader can create a zero-cost product.

Take a collar, for example. The trader combines a long position in a put with a lower strike price and a short position in a call with a higher strike price. If the premium received after selling the call offsets the premium paid for the put, the overall cost of the combined position is reduced to zero.

## Transforming a Standard American Option into a Nonstandard American Option

One of the most prominent characteristics of standard American options is the possibility to exercise them on or before the expiration date. However, there are certain things that could be done that effectively transform a standard option contract into a non-standard one. These include:

• Restricting early exercise to only a few specified dates
For example, a six-month American call could be exercisable only on the last day of each month. Such a restriction creates what’s called a Bermudan option.
• Imposing a lock-out period during which the option cannot be exercised
For example, a 3-month lockout period could be imposed on a six-month call. That means the holder is not allowed to exercise the option during the first three months of the contract.
• Having multiple strike prices in different phases of a contract
For example, a three-year call could be characterized by strike prices of $30 in the first year,$35 in the second year, and \$40 in the final year.

## Exotic Options

### Gap options

A gap option has a strike price, $${ K }_{ 1 }$$, and a trigger price, $${ K }_{ 2 }$$. The trigger price determines whether or not the option will have a nonzero payoff. The strike price determines the actual amount of the payoff. For a gap call option, the payoff will always be nonzero (positive or negative) as long as the final stock price exceeds the trigger price. For a gap put option, the payoff will always be nonzero as long as the final stock price is less than the trigger price. If $${ K }_{ 1 }={ K }_{ 2 }$$, the gap option payoff will be the same as that of an ordinary option.

When $${ K }_{ 2 }>{ K }_{ 1 }$$,

$$Gap\quad call\quad option\quad payoff=\begin{cases} { S }_{ T }-{ K }_{ 1 } & if\quad { S }_{ T }>{ K }_{ 2 } \\ 0\quad \quad \quad \quad & if\quad { S }_{ T }\le { K }_{ 2 } \end{cases}$$

Where:

$${ K }_{ 1 }$$=strike price

$${ K }_{ 2 }$$=trigger price

### Example

Let’s say $${ K }_{ 1 }$$ = 100 and $${ K }_{ 2 }$$ = 105. This would mean the trigger price exceeds the strike price.

At expiration, we’ll have the following payoffs:

 Stock Price 96 100 104 105 112 Call price 0 0 0 5 12

If the trigger price is less than the strike price for a gap call option, negative payoffs are possible.

### Example

Let’s say $${ K }_{ 1 }$$ = 108 and $${ K }_{ 2 }$$ = 100. This would mean the trigger price exceeds the strike price.

At expiration, we’ll have the following payoffs:

 Stock Price 96 100 106 108 112 Call Price 0 -8 -2 0 4

We can see that between stock prices of 100 and 108 at expiration, the payoff to the call option holder is negative.

$$Gap\quad put\quad option\quad payoff=\begin{cases} { { K }_{ 1 }-S }_{ T } & if\quad { S }_{ T }<{ K }_{ 2 } \\ 0\quad \quad \quad \quad & if\quad { S }_{ T }\ge { K }_{ 2 } \end{cases}$$

If the trigger price is greater than the strike price for a gap put option, negative payoffs could occur.

### Forward start options

As the words suggest, a forward start option kicks off at some point in the future. For example, today a trader may purchase a six-month put that will only come into effect three months from today. Forward start in-the-money options are usually used as incentives to boost employee productivity and encourage employee loyalty.

### Compound options

A compound option is simply an option on an option,i.e., an option for which the underlying is another option. A compound option can take one of four different forms:

• A call on a call (CoC) gives the investor the right to buy a call option at a set price for a set period of time.
• A call on a put (CoP)gives the investor the right to buy a put option at a set price for a set period of time.
• A put on a call (PoC) gives the investor the right to sell a call option at a set price for a set period of time.
• A put on a put (PoP) gives the investor the right to sell a put option at a set price for a set period of time.

### Chooser options

In a chooser option, the holder is allowed to decide whether it is a call or a put prior to the expiration date. The choice between the two depends in large part on the value of each.

### Barrier options

A barrier option is an option whose existence depends upon the underlying asset’s price reaching a predetermined barrier level. It can be either:

• A knock-out, implying it expires worthless if the underlying exceeds a certain specified price, effectively limiting profits for the holder but limiting losses for the writer.
• A knock-in, implying it has no value until the underlying reaches a certain specified price.

### Binary options

In a binary option, the payoff is either a fixed monetary amount or nothing at all. Binary options are of two types:

• Cash-or-nothing option which pays a fixed amount of cash if the option expires in-the-money
• Asset-or-nothing option which pays an amount equivalent to the value of the stock when the contract is initiated if the option expires in-the-money.

### Lookback options

A lookback option allows the holder to exercise an option at the most beneficial price of the underlying asset, over the life of the option.

### Shout options

In a shout option, the holder can lock profits at defined intervals while maintaining the right to continue participating in gains without a loss of locked-in profits.

### Asian options

In an Asian option, the payoff depends on the average price of the underlying asset over a period of time as opposed to standard options where the payoff is determined by the price of the underlying at a specific point in time.

### Exchange options

An exchange option gives the right but not the obligation to exchange money denominated in one currency, say, the USD, into another currency, say, the Euro, at a pre-set exchange rate on a specified date.

A basket option gives the right but not the obligation to buy or sell a basket of securities. The components of the basket could be bonds, stocks, currencies, e.t.c., and may be specified in advance.

## Volatility and Variance Swaps

In a volatility swap, volatility is exchanged based on a notional principal. Similarly, a variance swap involves the exchange of variance – the square of volatility – based on a notional principal. Volatility and variance swaps do not bet on the price of the underlying.

Variance swaps can be replicated using a collection of puts and calls. They are easier to price compared to volatility swaps.

## Hedging Exotic Options

Hedging of exotic options can be done by creating a delta neutral position and rebalancing frequently to maintain delta neutrality. However, some exotic options such as barrier options are relatively difficult to hedge. To hedge a barrier option, the portfolio that replicates its boundary conditions must be shorted and unwound when any part of the boundary is reached. The advantage of static options replication is that it does not require frequent rebalancing.

## Question

A cash-or-nothing call option has a payout profile equivalent to zero or:

1. The underlying asset price if the value of the asset ends below the strike price.
2. The underlying asset price if the value of the asset ends above the strike price
3. A set amount if the value of the underlying asset ends below the strike price
4. A set amount if the value of the underlying asset ends above the strike price.