properties of stock option questions
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Properties of Stock Option QuestionsTRANSCRIPT
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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.
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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
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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.