FRM Part I · FRM Exam Part I · Exotic Options
A cash-or-nothing call option pays USD 50 if the underlying asset price is above the strike at expiry and nothing otherwise. Under risk-neutral valuation, the risk-neutral probability that the asset finishes above the strike is 0.40, and the continuously compounded risk-free rate is 5% per year with one year to expiry. What is the value of the option, to the nearest cent?
The option is worth USD 19.02. Its value is the discounted risk-neutral expected payoff: 0.40 times USD 50 equals USD 20, discounted for one year at 5% continuous compounding by multiplying by e^-0.05, which gives about USD 19.02.
- AUSD 19.02Correct
- BUSD 20.00
- CUSD 21.03
- DUSD 30.12
Explanation
Value = e^(-0.05) x 0.40 x 50 = 0.951229 x 20 = USD 19.02. USD 20.00 omits discounting. USD 21.03 compounds the payoff upward instead of discounting. USD 30.12 uses probability 0.60 with discounting (0.951229 x 30).
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