An exotic option allows the holder, at time T to receive (with no further pay- ment)...

 

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An exotic option allows the holder, at time T to receive (with no further pay- ment) either a vanilla call or a vanilla put, both of which have the same expiry T>T and strike price Q. i. Show that prior to T this exotic option is equivalent to a portfolio of European calls with strikes and expiries which you should specify. ii. Derive the pricing formulation of this option. iii. At time 2, its holder will choose whether it becomes a European call or European put option, where each will expire at time 3 with a strike price of $75. At time 0, this option's price is $32.5, the underlying asset price is $60, and the risk-free rate is 4.7%. If C(0,T,Q) denotes the price of a European call option with strike price Q and maturity T, find C(0,3,75) where C(0,2,75e-2r) = $9. iv. Explain what happens as T 0. An exotic option allows the holder, at time T to receive (with no further pay- ment) either a vanilla call or a vanilla put, both of which have the same expiry T>T and strike price Q. i. Show that prior to T this exotic option is equivalent to a portfolio of European calls with strikes and expiries which you should specify. ii. Derive the pricing formulation of this option. iii. At time 2, its holder will choose whether it becomes a European call or European put option, where each will expire at time 3 with a strike price of $75. At time 0, this option's price is $32.5, the underlying asset price is $60, and the risk-free rate is 4.7%. If C(0,T,Q) denotes the price of a European call option with strike price Q and maturity T, find C(0,3,75) where C(0,2,75e-2r) = $9. iv. Explain what happens as T 0.

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