Question

25. The price of a stock with no dividends, is $35 and the strike price of a 1year European call option on the stock is $30. The risk-free rate is 4% (continuously compounded). Compute the lower bound for the call option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Please show your work. 26. A stock price with no dividends is $50 and the strike price of a 1-year European put option is $54. The risk-free rate is 5% (continuously compounded). Compute the lower bound for the put option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Please show your work. 27. The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is 6-month. Using the put-call parity, compute the price of a 6- month European put option on the stock with a strike price of $50. Please show your work.

Answer 1

25. We are required to calculate the minimum price of the European Call Option

Minimum =  Max(0,S-X/(1+rf)^T-t)

= Max(0,(35-30)/e^0.04) = $4.804

26. We are required to calculate the minimum price of the European Put Option.

Minimum = Max(0, X/(1+rf)^T-t – S)

= Max(0, 54/(e^0.05) – 50) = $1.366

27. Call Put Parity = Call option + Present Value of Strike Price = Put Option + Spot price

Present Value of Strike Price = Strike Price / (e)^r*t

= 50/e^0.06*0.5

= $ 48.52

Call Put Parity = $ 6 + $ 48.52 = Put Option + $ 51

Put Option = $ 3.52