Consider delta and gamma hedging a short call option, using the underlying and a

Question

Consider delta and gamma hedging a short call option, using the underlying and a put with the same strike and maturity as the call. Calculate the position in the underlying and the put that you should take. Will you ever need to adjust this hedge? Relate your result to put-call parity.

Asset price S0 50 Exercise price K 40 Interest rate r 0.05 Volatility sigma 0.3 Dividend yield q 0.02 Time to maturity T 2 Expected return mu 0.12 Number of simulations M 1000 Number of time periods N 20 Percentage pct 0.05

Explanation / Answer

In financial mathematics put call parity defines a relationship between the price of a European call option and European put option,both with the identical strike price and expiry,namel that a portfolio of a long call option and a short put option is equivalent to single forward.

equation is C+X/(1+r )*t=s+p

where c= call premium

p=put premium

x=strike price of a call and put

r= annual interest rate

t= time period

s= initial price

In this case a delta neutral trading strategy involves the purchase of a theoretically underpriced option while taking an opposite position in the underlying futures contract.

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