IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model
A one-year European digital option pays Rs 100 if the share price at expiry exceeds the strike, else nothing. Under Black-Scholes with r = 5% continuously compounded, the risk-neutral probability that S_T exceeds the strike is 0.60. Using e^-0.05 = 0.9512, what is the option's value today?
The value is the discounted risk-neutral expected payoff: 100 times 0.60 times e to the power minus 0.05, which equals about Rs 57.07. Using the real-world probability or omitting discounting would give a wrong answer.
- ARs 60.00
- BRs 57.07Correct
- CRs 62.93
- DRs 95.12
- Rs 5.71
Explanation
Value = e^(-rT) x E_Q[payoff] = 0.9512 x 100 x 0.60 = 57.07. Rs 60 omits discounting. Rs 62.93 would divide instead of multiply, and Rs 95.12 ignores the probability.
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