Question

A short forward contract on an asset plus a long position in a European call option on the asset with a strike price equal to the forward price is equivalent to

a)A short position in a call option

b)A short position in a put option

c)A long position in a put option

d)None of the above

Answer 1

Hi

This is a hedged portfolio, in which if the asset price goes above the strike price, call option will become profitable but forward contract will be in loss.

on the other hand, if asset price goes below is the strike price then call option will become null and forward contract will be in profit.

Let F is forward price and S is asset price at maturity and X is strike price.

so payoff from short forward contract = F-S

payoff from long call will be (S-X,0)  

Also here F = X

So the payoff is (X-S + S-X , X,S)

= (0,X-S)

Which is similar to long position in put option option.

Hence option c is correct here.