Question

Show how Put-Call parity can be used to construct a synthetic stock. Show that the payoffs from the synthetic are identical to that of a stock.

Answer 1

Put-call parity is a principle that defines the relationship between the price of European put options and European call options of the same class, that is, with the same underlying asset, strike price, and expiration date.

The formula for put call parity is as follows

C + PV(x) = P + S

where:

C = price of the European call option

PV(x) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate

P = price of the European put

S = spot price or the current market value of the underlying asset