Question

1)

The current price of a stock is $15. In 6 months, the price will be either $18 or $13. The annual risk-free rate is 3%. Find the price of a call option on the stock that has a strike price of $14 and that expires in 6 months. (Hint: Use daily compounding.) Round your answer to the nearest cent. Assume a 365-day year. Do not round your intermediate calculations.

2)

The current price of a stock is $20. In 1 year, the price will be either $26 or $15. The annual risk-free rate is 3%. Find the price of a call option on the stock that has a strike price is of $24 and that expires in 1 year. (Hint: Use daily compounding.) Round your answer to the nearest cent. Assume 365-day year. Do not round your intermediate calculations.

Answer 1

1

Upmove (U)= High price/current price=18/15=1.2

Down move (D)= Low price/current price=13/15=0.8667

Risk neutral probability for up move

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

=(e^(0.03*0.5)-0.8667)/(1.2-0.8667)=0.44534

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(18-14,0)

=Max(4,0)

=4

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(13-14,0)

=Max(-1,0)

=0

Price of call option = (q*Payoff H+(1-q)*Payoff L)/(1+r)^(1/2)

=(0.445339*4+(1-0.445339)*0)/(1+0.03)^(1/2)

=1.76

Please ask remaining parts seperately, questions are unrelated