C15 EXOTIC OPTION

BASIC #

Exotic derivatives are customized to fit a specific firm need for hedging that cannot be met by plain vanilla derivatives.

Reasons for developing exotic derivatives:

1. Provide a unique hedge for a firm’s underlying assets.
2. Addressing tax and regulatory concerns.
3. Speculating on the expected future direction of market prices.

PACKAGES TO FORMULATE A ZERO-COST PRODUCT #

A package is defined as some combination of standard European options, forwards, cash & the underlying asset., example – straddle, bull, bear etc. Because packages often consist of a long position and at short position, they can be constructed so that the initial cost of the investor is zero.

TRANSFORMING STANDARD AMERICAN OPTIONS INTO NON STANDARD AMERICAN OPTIONS #

When some changes are made to standard feature of options, standard options become non standard options. Three common features that transform standard options into non-standard are:

1. Restrict early exercise to certain dates.   – Bermudan options.
2. Early exercise can be limited to a certain portion of the life of the option.
3. The options strike price may change.

EXOTIC OPTION PAYOFF STRUCTURES #

1. GAP OPTIONS : A gap option has two strike prices, X₁ & X₂ (trigger price).

• GAP CALL OPTION :- If X₂ > X₁

              If S_T > X₂ , Payoff = S_T  – X₁

                           S_T ≤ X₂ , Payoff = 0

If X₂ ≤ X₁      Payoff = X_{2 –}  X₁

• GAP PUT OPTION :- If X₂ < X₁

                      If S_T < X₂ , Payoff = X₁ –  S_T

                           S_T  ≥ X₂ , Payoff = 0

If X₂ ≥ X₁      Payoff = X_{2 –}  X₁

2. FORWARD START OPTIONS: Options that begin their existence at sometime in the future. Example: Employee incentive plan.
3. COMPOUND OPTIONS: Compound options are options on options. Compound options have two levels of the underlying that determines their value – the value of the underlying option which in turn is determined by the value of the underlying asset. It consists of two strike price & two exercise dates.

• A call on a call 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 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 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 gives the investor the right to sell a put option.

4. CHOOSER OPTIONS : Allows the owner to choose weather the options is a call or a put after a certain period of time.
5. BARRIER OPTIONS : Options whose payoff depends on weather the underlying’s asset price reaches a certain barrier level over the life of the option. Specific types of barrier options are:

• Down-and-out call (put). A standard call (put) option that ceases to exist if the underlying asset price hits the barrier level, which is set below the current stock value.
• Down-and-in call (put). A standard call (put) option that only comes into existence if the underlying asset price hits the barrier level, which is set below the current stock value.
• Up-and-out call (put). A standard call (put) option that ceases to exist if the underlying asset price hits a barrier level, which is set above the current stock value.
• Up-and-in call (put). A standard call (put) option that only comes into existence if the underlying asset price hits the above-current stock-price barrier level.

6. BINARY OPTIONS : Options payoff has one of two states: The option pays a set dollar amount at expiration if the option is above the strike price, or the option pays nothing if the price is below the strike price.

• Cash – or – nothing call : Fixed amount is paid if the asset ends up above the strike price.
• Asset – or – nothing call : Pays the value of the stock when the contract is initiated if the stock price ends up above the strike price at expiration.

7. LOOKBACK OPTIONS: Options whose payoff depends on the maximum or minimum price of the underlying asset during the life of the option

• Floating look back call: Pays minimum price – Expiration price
• Floating look back put : Maximum price – Expiration Price
• Fixed lookback call : It is identical to a European call option except the expiration price is the maximum price during the option’s life.
• Fixed lookback Put : Payoff is like European Put option but replaces the final stock price with the minimum price during the option’s life.

8. SHOUT OPTIONS : It allows the holder to receive either the intrinsic value of the option at the shout date or at expiration, whichever is greater.
9. ASIAN OPTIONS : Asian options have payoff profiles based on the average price of the security over the life of the option. Average price calls & puts payoff the difference between the average stock price & the strike price.
10. EXCAHNGE OPTIONS : It is used to exchange one currency with another.
11. BASKET OPTIONS : Options to purchase or sell baskets of securities. Basket may consist of specific stocks, indices or currencies.

VOLATILITY & VARIANCE SWAP #

• VOLATILITY SWAP : Exchange of volatility based on a notional principal.
• VARIANCE SWAP : It involves exchange a pre specified fixed variance rate for a realized variance rate.

ISSUES IN HEDGING EXOTIC OPTIONS #

Hedging exotic options requires replication of portfolio. It may require further futures adjustment  called Dynamic options replication. Dynamic options replication requires frequent trading which makes it costly to implement.

As an alternative, a static options replication is used in which a short portfolio of actively traded options is created which drastically reduces the transaction costs associated with dynamic rebalancing.