Question

Question 3 - (30 Points) (a) Assume that So = 10 EUR and r = 3% continuously compounded. The price of a 9-months European put option with strike K = 8 EUR is 2 EUR. Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6% per annum continuously compounded. The price for 6-months European put option with same strike, underlying and maturity is $2. What opportunities are there for an arbitrageur? Describe the strategy and compute the gain.

Answer 1

By put call paritty C+x - SotP 9 (149) Where ca call poremium poput premium 10 So - Initial price of underlying. X= Strike price of call and put " az annual interest rate t- time in years 12 (2) So=10 r- 3% X=8 P=2 t= 0.75425 (9 monous - By put call parity - ..c = So tp - xert = 10+2 - 8 -0.03*0.75 = 4.18 (b) r = 6% t-0.5yrs Comonins 4 c=3 So=50 X=55 According to put call parity p = {+ xert - Soon = 3 + 5ste o obxo :. xert - 5 6x05 - 50 -50 - 638 Market Hence price of put = 2 it is undervalued.