BY CHRIS DIBELLA Exotic Options

Options A financial derivative that represents a contract sold by one party to another. This contract offers the buyer the right to buy or sell a security at an agreed upon price during a certain period of time. Two types: Vanilla and Exotic

Exotic Options Term was popularized by Mark Rubinstein in 1990 Based on either exotic wagers in horse racing or from the use of exotic terms when naming options Options with more complex features than vanilla options Usually traded over the counter Directly between two parties Option can be tailored to fit any situation

Path Dependence vs. Independence Dependent Value of the option depends on the path the underlying takes Independent Value depends only on the value of the underlying when exercised or expired

Pricing Methods Expected payoff pricing Black-Scholes Method Binomial Trees Monte Carlo Methods Generate many random walks Average option values and discount to current prices

Asian Options Introduced in Tokyo, Japan in 1987 Payoff is determined by the average underlying price over a pre-set period of time Two Types: Fixed Strike Payoff is the difference between a set strike price and the average value of the underlying Floating Strike Payoff is the difference between the underlying value at expiration and the average underlying value

Examples Fixed StrikeFloating Strike

Why buy an Asian Option Want to cover many transactions using only one hedging instrument Reduce the dependence of an option on the spot price of the underlying on a single date Less expensive since the volatility of the average price is usually less than the volatility of the spot price

Binary Options aka digital options or all-or-nothing options Can be calls or puts, American or European Payoff is either a fixed amount or nothing Two Types Cash-or-nothing Pays fixed amount if the underlying is in the money Asset-or nothing Pays the value of the underlying

Pricing Cash or Nothing Payoff is a constant Asset or Nothing Payoff is the value of the underlying, S T

Barrier Options Similar to vanilla options – can be calls or puts, American or European Becomes active or inactive after the underlying crosses a certain point Knock-In Options-Option becomes active only if the underlying crosses the barrier Knock-Out Options-Option becomes void if the underlying crosses the barrier Once the underlying passes the barrier it does not matter if it passes it again

Example

Call Option Comparison You are looking to buy a call option on a stock with the following information: S0=100, K=100, r=.003, σ=.3, T=1.5 Vanilla Call Value - $14.77 What do you expect the value of the same call with a Knock-Out barrier, B=150, to be? As the barrier moves closer the strike price, what do you think will happen to the value of the option?

Barrier Price Knock-Out Barrier Option Price

Why buy a Barrier Option? Cheaper than a plain call or put Creates opportunity for greater profits Expect movement within a limited range Disadvantages Knock-Out Too much movement could void an option Knock-In Option can be out of the money even when it has passed the strike price

Lookback Options Created in 1979 by Robert C. Merton Calls or Puts Allows holder to lookback for the optimal values Two Types: Fixed Strike Payout is difference between strike price and the maximum or minimum value of the underlying Floating Strike Payout is difference between underlying value at expiration and the maximum or minimum value of the underlying

Example

Call Option Comparison You are looking to buy a call option on a stock, with the following information: S0=100, K=100, r=.003, σ=.3, T=1.5 Vanilla Call Value - $14.77 Knock-Out Call Value - $3.51 What do you expect the value of the same call with a fixed strike lookback?

Why buy a Lookback Option Eliminates any timing problems Maximizes payoff Disadvantages Expensive

Other Exotic Options Chooser Option Allows holder to choose whether it is a call or put at a particular date Rainbow Option Option linked to two or more underlying values Shout Options Option that allows holder to adjust aspects of the option at certain intervals, such as the strike price or time to maturity

Sources Option Calculator