FRM Part I · FRM Exam Part I · Options Markets
A box spread uses strikes 40 and 50 on European options expiring in exactly 1 year: long 40 call, short 50 call, long 50 put, short 40 put. The continuously compounded risk-free rate is 4%. Assuming no arbitrage, what is the approximate value of the box today? (e^-0.04 = 0.9608)
The box spread is worth about USD 9.61. Its payoff at expiry is a certain USD 10, the difference between strikes, so its no-arbitrage value is that amount discounted one year at 4% continuous compounding: 10 times 0.9608.
- AUSD 10.00
- BUSD 9.61Correct
- CUSD 9.00
- DUSD 10.41
Explanation
A bull call spread plus a bear put spread has a certain payoff of 50 - 40 = 10 at expiry regardless of price. Its no-arbitrage value is the present value: 10 x 0.9608 = 9.61. Using 10 ignores discounting, and 10.41 compounds in the wrong direction.
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