Question

A stock price is currently $50. It is known that at the end of 6 months it will be either $45 or $55. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a 6-month European put option with a strike price of $50?

Answer 1

Upmove (U)= High price/current price=55/50=1.1

Down move (D)= Low price/current price=45/50=0.9

Risk neutral probability for up move

q = (e^(risk free rate*time)-D)/(U-D)

=(e^(0.1*0.5)-0.9)/(1.1-0.9)=0.75636

Put option payoff at high price (payoff H)

=Max(Strike price-High price,0)

=Max(50-55,0)

=Max(-5,0)

=0

Put option payoff at low price (Payoff L)

=Max(Strike price-low price,0)

=Max(50-45,0)

=Max(5,0)

=5

Price of Put option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)

=e^(-0.1*0.5)*(0.756355*0+(1-0.756355)*5)

=1.16