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?
Put Call Parity Equation
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
Value of an European Put with same maturity and strike price as A option will be =$3,34
For Synthetic Put:
.1 Short stock
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
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