FRM Part I · FRM Exam Part I · Trading Strategies
A box spread is built from European options with strikes K1=40 and K2=50, expiring in one year. The continuously compounded risk-free rate is 4%. Using e^-0.04 = 0.9608, what is the no-arbitrage value of the box spread today, and what is the payoff at expiry?
The box spread is worth about 9.61 today and pays a certain 10 at expiry. Its payoff is always the strike difference, 10, so the no-arbitrage value is that amount discounted one year at 4% continuous compounding.
- AValue 10.00; payoff 10
- BValue 9.61; payoff 10Correct
- CValue 9.61; payoff 9.61
- DValue 10.41; payoff 10
Explanation
A box spread (bull call spread plus bear put spread) pays K2-K1 = 10 at expiry in every scenario. Its present value is 10 × 0.9608 = 9.61. The 10.41 option compounds forward instead of discounting.
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