The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. Risk-free interest rates for all maturities are 10%. What is the price of a European put option that expires in six months and has a strike price of $30?

The price of put option is $2.51

Explanation:

The relation between the European Put option and Call option is called the Put-Call parity. Put-Call parity will be employed to solve the question

According to Put-Call parity, P = c - Sо + Ke^(-n) + D. Where P=Put Option price, C=Value of one European call option share. Sо = Underlying stock price,  D=Dividend, r=risk free rate, t = maturity period

Value of one European call option share = $2

Underlying stock price = $29

Dividend = $0.50

Risk free rate = 10%

Maturity period = 6 month & 2 month, 5 month when expecting dividend

P = c - Sо + Ke^(-n) + D

P = $2 - $29 + [$30 * e^[-0.10*(6/12)] + [$0.50*e^(-0.10*(2/12) + $0.50*e^(-0.10*(5/12)]

P = $2 - $29+($30*0.951229) + ($0.50*0.983471 + $0.50*0.959189)

P = -$27 + $28.5369 + $0.4917 + $0.4796

P = $2.5082

P = $2.51

Therefore, the price of put option is $2.51

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