FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at 40. After one period it will be either 50 or 32. The risk-free rate is 5% per period (simple, one-period compounding). Using risk-neutral valuation, what is the value of a European call with strike 42 expiring at the end of the period?
The call is worth about 4.23. The risk-neutral up probability is 5/9, the up payoff is 8 and the down payoff is 0. The expected payoff of 4.44 is discounted one period at 5%, giving 4.23. A replicating portfolio gives the same value.
- A4.23Correct
- B4.44
- C3.81
- D4.67
Explanation
u = 1.25 and d = 0.80, so p = (1.05 - 0.80)/0.45 = 5/9. The payoffs are 8 up and 0 down. Value = (5/9 × 8)/1.05 = 4.23, and replication (delta 0.4444, borrowing 13.545) confirms it. 4.44 omits discounting. 3.81 uses p = 0.5. 4.67 multiplies by 1.05 instead of dividing.
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