Question

A stock price is currently $50. A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. Use two-period binomial models to value the six-month options on this stock. Remember to show detailed calculations of the option value at each node.

(a) What is the value of a six-month European call option with a strike price of $51?

(b) What is the value of a six-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put–call parity.

(c) If the put option in part (b) of this question were American, would it ever be optimal to exercise it early at any of the nodes on the tree?

Answer 1

a

b

c

As per put call parity

Call price + PV of exercise price = Spot price + Put price

1.6351+51*e^(-0.05*0.5)=50+Put value

Put value = 1.3759

d

No because in step 6 and step 4 payoff/final value (35.;5.875) is more than price in step 7(1.6456) . Thus there is a possibility of higher payoff if you wait