Question

Use the following information to answer Questions 1 to 6 (please show working)

.A European call option on a non-dividend paying stock has an exercise price of $10 and six months to expiration. The current price of the stock is $10 and the stock price is expected to rise or fall by 10% during each three-month period. The risk-free rate is 5% p.a. (c.c.).

1. If the stock price rises for two consecutive periods, the expiration date stock will be: (a) $8.10 (b) $11.00 (c) $9.90 (d) $12.10. 18

2. The risk-neutral probability of an uptick is: (a) 0.5000 (b) 0.5630 (c) 0.4370 (d) 0.6000.

3. The probability of two successive upticks is: (a) 0.3170 (b) 0.2500 (c) 0.1910 (d) 0.3600.

4. The hedge portfolio at time 0 comprises one short call option and: (a) short one share (b) long 0.5838 shares (c) short 0.6266 shares (d) long 0.5250 shares.

5. The expiration date payoff on the call option after one uptick and one downtick is: (a) $2.10 (b) -$0.10 (c) $0.00 (d) -$1.90.

6. The two-period binomial option pricing model will value the call option at time 0 at: (a) $0.649 (b) $0.633 (c) $0.391 (d) $0.657.

Answer 1

(4) Under binomial model Delta = (cu-cd) / (us-ud) = (11-0)/(11-9) = 11/2 = 0.55.Therefore to hedge one call option we will buy 0.5250 shares.Therefore option D is correct.

(5) Pay off at expiration = $12.1 - $ 10 = $2.1 therefore option A is correct.