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Option and Value

Decent Essays

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. …show more content…

(a) In this case, change in t = 0.25 so that

u = e0.40 x √0.25 = 1.2214, d = 1/u = 0.8187, a = e0.03 x 0.25 = 1.0075, and p = (1.0075 – 0.8187) / (1.2214 – 0.8187) = 0.1888/0.4027 = 0.4688
(b) The price of this stock at node A is 50;

The price of this stock at node B is 50u = 50*1.2214 = 61.07;
The price of this stock at node C is 50d = 50*0.8187 = 40.93;
The price of this stock at node D is 50*u*u = 50*1.2214*1.2214 = 74.59;
The price of this stock at node E is 50*u*d = 50;
The price of this stock at node F is 50*d*d = 50*0.8187*0.8187 = 33.51;
The value of the put option at node D is 0;
The value of the put option at node E is 5;
The value of the put option at node F is 21.49;
The value of the put option at node B is e-0.03 x 0.25[0.4688*0+(1-0.4688)*5] = 2.63;
If no early exercise, the value of the put option at node C would be e-0.03 x 0.25[0.4688*5+(1-0.4688)*21.49] = e-0.03 x 0.25[2.3440+11.4155] = 13.66;
If early exercise at node C, the payoff of the American put option should be 14.07;
Thus, it is optimal to early exercise at node C, and the value of the put option at node C is 14.07.
If no early exercise, the value of the put option at node A is e-0.03 x 0.25[0.4688*2.63+(1-0.4688)*14.07] = e-0.03 x 0.25[1.23+7.47] = 8.64 ;
If early exercise at node A, the payoff of the American put option should be 5;
Thus, it is optimal to wait at node A and the put option at node

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