FRM Part I · FRM Exam Part I · Trading Strategies
A box spread consists of a bull call spread with strikes K1 = 50 and K2 = 60 and a bear put spread with the same strikes, all European and with one year to maturity. The continuously compounded risk-free rate is 5%. Which price for the box spread is consistent with no arbitrage (closest value)?
The no-arbitrage price is about $9.51. A European box spread always pays the difference between strikes, $10, at expiry, so its value today is that certain payoff discounted at 5% for a year: 10 times e to the minus 0.05.
- A$10.00
- B$9.51Correct
- C$10.51
- D$5.00
Explanation
A box spread payoff is always K2 - K1 = 10 at expiry. Its no-arbitrage value is the present value: 10 × e^(-0.05) = 9.512. Paying $10.00 ignores discounting; $10.51 compounds the wrong way.
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