IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model
A non-dividend-paying share trades at Rs 100. A European call with strike Rs 100 and one year to expiry is priced by Black-Scholes at Rs 12.00 when the continuously compounded risk-free rate is 5%. Using put-call parity, with e^(−0.05) = 0.9512, what is the price of the European put with the same strike and expiry?
The put is worth Rs 7.12. Put-call parity gives P = C − S + K·e^(−rT) = 12 − 100 + 95.12, since the discounted strike is 100 × 0.9512 = 95.12.
- ARs 7.12Correct
- BRs 12.00
- CRs 4.88
- DRs 9.76
- Rs 17.12
Explanation
Put = C − S + K·e^(−rT) = 12 − 100 + 95.12 = 7.12. Rs 17.12 arises from the wrong sign on the discounted strike. Rs 4.88 arises from using K(1 − e^(−rT)) without S adjustments, i.e. 100 − 95.12.
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