The current price of a non-dividend-paying biotech stock is $140 with a volatili

Question

The current price of a non-dividend-paying biotech stock is $140 with a volatility of 24%. The risk-free rate is 4%. A trader is using a two-step binomial tree to value a 6-month European call option. The strike price is $150. A. What are the up- and down-movement u and d? B. What are the probabilities of an up- and down-movement in a risk-neutral world? C. What is the value of the European call option? D. Suppose that a trader sells 10,000 European call options. What position should the trader take to hedge the position for the first three-month period? (Hint: You need to find the delta for the first three-month period. Do not use the Black-Scholes delta.)

Explanation / Answer

Solution:

A. u = e^0.24*.24 = 1.1248. The percentage up movement is 12.48%

d = 1/u = 1/1.1248 = 0.8891. The percentage down movement is 11.09%

B. The probability of an up movement is (e^0.04*0.24 – 0.8891)/(1.1248 – 0.8891) = 0.5114

The probability of a down movement is 1 – 0.5114 = 0.4886

C. c= e^-0.04x0.5/2[0.5114´15+0.4886´0]= 7.595

D. The delta for the first period is 15/(140*1.1248 – 140*0.8891) = 0.4548. The trader should take a long position in 4,548 shares.

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