FRM Part I · FRM Exam Part I · Exotic Options
A chooser option lets its holder choose at time T1 = 1 year whether it becomes a European call or put, both with strike 100 and expiry T2 = 2 years. The asset pays no dividend and the continuously compounded risk-free rate is 5%. The chooser can be replicated by a call with strike 100 and expiry T2, plus a put expiring at T1. What strike should the put have?
The put strike is 95.12. Because max(c,p) equals the call plus a put struck at the discounted strike, K·e^(−r(T2−T1)) = 100·e^(−0.05) ≈ 95.12, expiring at the choice date.
- A95.12Correct
- B100.00
- C97.56
- D105.13
Explanation
At T1 the chooser equals max(c, p). Put-call parity gives c = p + S − K·e^(−r(T2−T1)), so max(c,p) = c + max(0, K·e^(−r(T2−T1)) − S). That is a put with strike 100·e^(−0.05) = 95.12 expiring at T1. Strike 105.13 reverses the sign, and 100 ignores discounting.
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