CFA Level I · CFA Level I Exam · Pricing and Valuation of Options
A stock trades at 50. In a one-period binomial model it can rise to 60 (u = 1.20) or fall to 40 (d = 0.80). The risk-free rate is 5% for the period. A European call has a strike of 50. The value of the call today is closest to:
The call is worth about 5.95, found with a risk-neutral probability of 0.625, a payoff of 10 in the up state, and discounting at 5%.
- A3.97
- B4.76Correct
- C5.24
Explanation
Risk-neutral probability of an up move = (1.05 − 0.80)/(1.20 − 0.80) = 0.625. The call pays 10 in the up state and 0 in the down state. Value = 0.625 × 10 / 1.05 = 5.95. Check by hedge: delta = 10/20 = 0.5; portfolio long 0.5 shares and short 1 call costs 25 − c and pays 20 in both states, so 25 − c = 20/1.05 = 19.05, giving c = 5.95. The keyed option must therefore be 5.95, which is not listed; corrected options needed.
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