Option and Value

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1. _____ is the rate of change of delta with respect to the price of the underlying asset. a. Gamma
b. Theta
c. Rho
2. The short term risk-free rate usually used by derivatives traders is b. The LIBOR rate
3. Duration of a ten-year 6% coupon bond with a face value of $100 is a. Less than 10 years.
4. Which of the following are always positively related to the price of a European call option on a stock? c. The volatility
5. When we talked about Vega hedging, if a portfolio has 1000 shares of SPY and 10 contracts of at-the-money December 2013 put option on SPY (and nothing else in the portfolio), is the portfolio vega neutral? c. No, the portfolio can never be vega neutral.

6. Which of the following is not true?
a. When a CBOE option on IBM is exercised, IBM issues more stock 7. Which of the following is not true?
a. Futures contracts nearly always last longer than forward contracts 8. In the corn futures contract a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true? b. This flexibility tends decrease the futures price.

9. Which of the following is true?
b. The principal amounts usually flow in the opposite direction to interest payments at the beginning of a currency swap and in the same direction as interest payments at the end of the swap. 10. A trader sells 10 call option contracts on a certain stock. The option price is $10, the stock price is $50, and the option’s delta is 0.65. How can the trader hedge the short position so that the portfolio is delta-neutral? b. The trader needs to buy 650 shares. 0.65 * (-10)*100 = - 650. buy 650 shares to create a delta-neutral position. 11.What is the price of an American call option on a non-dividend-paying stock when the stock price is $180, the strike price is $200, the risk-free interest rate is 5% per annum, the volatility is 30% per annum, and the time to maturity is 2 years? a. What is the value of S0, K, r, σ, T, d1 and d2?

b. You are expected to use the attached Normal distribution table to find out N(d1) and N(d2). What is the price of this American call option? a. In this case S0 = 180, K = 200, r = 0.05, σ = 0.30 and T = 2 d1 = [ln(180/200) + (0.05 + 0.32/2)2] / (0.30√2) = (-0.1054 + 0.1900)/0.4243 = 0.1994. d2 = d1 – 0.30√2 = 0.1994 – 0.4243 = -0.2249.

b. N(d1)= 0.5791 and N(d2)= 0.4110. therefore the price of the European call is

180N(d1) – 200e-0.05 x 2 N(d2) = 180*0.5791 – 200*0.9048*0.4110 = 104.238 – 74.3746 = 29.8634

11. (Please keep your numbers to the 4 digits.) What is the price of an American call option on a non-dividend-paying stock when the stock price is $180, the strike price is $200, the risk-free interest rate is 5% per annum, the volatility is 30% per annum, and the time to maturity is 2 years? More specifically,

a. What is the value of S0, K, r, σ, T, d1 and d2?

b. You are expected to use the attached Normal distribution table to find out N(d1) and N(d2). What is the price of this American call option?

Answer:
a. In this case S0 = 180, K = 200, r = 0.05, σ = 0.30 and T = 2

d1 = [ln(180/200) + (0.05 + 0.32/2)2] / (0.30√2) = (-0.1054 + 0.1900)/0.4243 = 0.1994. d2 = d1 – 0.30√2 = 0.1994 – 0.4243 = -0.2249.
b. N(d1)= 0.5791 and N(d2)= 0.4110. therefore the price of the European call is

180N(d1) – 200e-0.05 x 2 N(d2) = 180*0.5791 – 200*0.9048*0.4110 = 104.238 – 74.3746 = 29.8634 Derivatives Fall 2012 Final Exam: December 12th, Wednesday 10:10 am – 12:10 pm

12. Consider an American put option on a non-dividend-paying stock where the stock price is $50, the strike price is $55, the risk-free rate is 3% per annum, the volatility is 40% per annum, and the time to maturity is six months.

a. Calculate u, d, a, and p for a two-step tree.
b. Value the option using a two step tree, more specifically, please show the price of this stock at each of...
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