Properties of Stock OptionWorksheet

10-Feb-111. What is the lower bound for the price of a six month call option on a non-dividend

paying stock when the stock price is $80 and the strike price is$ 75, and the risk-free rate of interest is 10% per annum?

The lower bound is 80 – 75e – (0.1*0.5) = $[80 – 75(0.951229)]= $ 8.65782Or $8.66

2. What is the lower bound of a two month European put Option on a non-dividend paying stock when the stock price is$58 and the strike price is $65, and the risk-free rate of interest is 5%?

The lower bound is 65(e –(0.1667*0.05) – 58 = $ 6.46

3. A four month European call option on a dividend paying stock is currently selling for $5. The stock price is $64 and the strike price is $60, and dividend of $0.80 is expected in one month. The risk free-rate of interest is 12% per annum for all maturities. What opportunities are there for an arbitrageur?

4. The price of an American call on a non-dividend paying stock is $4. The stock price is $31, the strike price is $30, and the expiration date is in 3 months. The risk free rate of interest is 8%. Derive the upper and lower bounds for the price of the American put with the same strike price and expiration date and same underlying stock.

5. What is the lower bound for the price of a one month European put option on a non-dividend paying stock when the stock price is $ 12 and the strike price is $15, and the risk free rate of interest is 6% per annum.

The lower bound is Ke-rT- S0 = 15e (-0.06*0.0833) - 12 = $ (15 * 0.995014) – 12 = $ 2.925217

6. Using the Black-Scholes model obtain the values of the put and call options from the following data from the following:-

Price of the share Rs.124Exercise Price Rs.130Time to maturity 4 monthsRisk free rate of interest 12% p aVolatility 5%Verify if the put call parity holds.

7. Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $29, the risk –free rate is 5%, the volatility is 25% per annum, and the time to maturity is four months.

a) What is the price of the option if it is a European call?b) What is the price of the option if it is an America call?c) What is the price of the option if it is a European put?d) Verify that put call parity holds.

8. A European call option and put option on a stock both have a strike price of Rs.20 and expiration date of 3 months. Both sell for Rs.3. The risk free rate of interest is

10% per annum. The current stock price is Rs. 19 and Rs 1 dividend is expected in one month Identify the arbitrage opportunity open to a trader.