FRM Part I · FRM Exam Part I · Trading Strategies
A box spread is built from European options on a non-dividend-paying stock with strikes K1 = 40 and K2 = 50, expiring in one year. The continuously compounded risk-free rate is 5%. Using no-arbitrage pricing, what is the fair value of the long box spread today (bull call spread plus bear put spread)?
The fair value is about $9.51. A long box spread has a certain payoff equal to the strike difference, $10, at expiry, so its no-arbitrage value is that amount discounted one year at 5% continuous compounding: 10 × e^-0.05 ≈ 9.51.
- A$10.00
- B$9.51Correct
- C$9.76
- D$10.51
Explanation
A box spread pays K2 - K1 = 10 with certainty at expiry regardless of the stock price. Its value is the present value: 10 × e^(-0.05) = 10 × 0.951229 = $9.51. Using $10 ignores discounting; $10.51 compounds in the wrong direction.
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