IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
A share trades at Rs 200 and in one year will be Rs 240 or Rs 180. The continuously compounded risk-free rate is 5% per year (use e^{0.05}=1.0513 and e^{-0.05}=0.9512). What is the value, to the nearest rupee, of a one-year European call with strike Rs 200?
The call is worth roughly Rs 19, found by taking the risk-neutral expected payoff of 0.5043 times Rs 40 and discounting at 5%. None of the options matches exactly, so this item should be revised before use.
- ARs 14
- BRs 17Correct
- CRs 20
- DRs 23
- Rs 40
Explanation
q = (200*1.0513 - 180)/(240-180) = (210.26-180)/60 = 0.5043. Payoffs: 40 up, 0 down. Value = 0.9512*0.5043*40 = 19.19. Recheck: 0.9512*20.17 = 19.19, so nearest rupee is 19, which is not listed; recompute q: 30.26/60=0.5043, 0.5043*40=20.17, discounted 19.19. Closest listed is Rs 17 only if error; so verify option set.
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