Question

Imagine that you are unable to short-sell a particular stock. Using put-call parity, replicate a short position in the stock, assuming that the stock pays no dividends,

there is a put and a call option, both of which have the same exercise price, K, and the same time to expiration, T. You are able to borrow and lend the

continuously compounded risk free rate, r.

Answer 1

Put - Call parity can be termed as :

Where C = Position in a call option,

KerT = Position in the bond with face value equal to the strike price of the option K, invested at r(continuous compounded risk free rate) for time period T (option expiration T).

P = Position in the put option

and, S = Position in the stock.

Given to us that we need to derive the parity in such a way that we are able to short the stock. The equation for the same is:

S- refers to taking a short position in the stock. This can be done by simply taking a LONG POSITION in the PUT OPTION (P+), a SHORT POSITION IN CALL OPTION and BORROWING MONEY equal to the strike price K for time period T at risk free rate r.