Question

Suppose that a 6-month European call A option on a stock with a strike price of $75 costs $5 and is held until maturity, and 6-month European call B option on a stock with a strike price of $80 costs $3 and is held until maturity. The underlying stock price is $73 with a volatility of 15%. Risk-free interest rates (all maturities) are 10% per annum with continuous compounding.

Use put-call parity to explain how would you construct a European put with the same maturity and strike price as European call A option. What is the price of the synthetic put?

Answer 1

Put Call Parity Equation

C+X/(e^(rt))=S0+P

C=Call premium=$5

P=Put premium

X=Strike price of Put and Call=$75

r=annual interest rate=10%=0.1

t=Time in years=0.5(Six months)

S0=Initial price of underlying=$73

5+75/(e^(0.1*0.5)=73+P

5+71.34=73+P

P=$3.34

Value of an European Put with same maturity and strike price as A option will be =$3,34

For Synthetic Put:

.1 Short stock

2.Buy Call

Price of Synthetic put =$5

The payoff will be same as Put.

If the stock price goes down, there will be gain on shorting stock , but Zero Payoff for Call option

If stock price goes up, there will be loss on shorting stock which will be compensated by gain on Call Option