CMA Final · Strategic Financial Management · Options
A share is at ₹100. In a one-period binomial model it can rise to ₹125 or fall to ₹80. A call has strike ₹105. The risk-free rate for the period is 5%. What is the value of the call today (using the risk-neutral approach)?
The call is worth ₹10.58. The risk-neutral up probability is 0.25 divided by 0.45, or 0.5556. Expected payoff is 0.5556 times 20, equal to 11.11, which discounted at 5% gives about ₹10.58.
- A₹8.57Correct
- B₹10.58
- C₹12.38
- D₹6.35
Explanation
Up = 1.25, down = 0.80. p = (1.05 - 0.80)/(1.25 - 0.80) = 0.25/0.45 = 0.5556. Payoff up = 125 - 105 = 20, down = 0. Call = 0.5556 x 20 / 1.05 = 11.11/1.05 = ₹10.58. This corresponds to the second option, so the key is 10.58.
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