FRM Part I · FRM Exam Part I · Trading Strategies
A European box spread with strikes 80 and 100 and one year to maturity is quoted at $18.00. The continuously compounded risk-free rate is 4%. Which action captures an arbitrage profit, and what is the present value of the profit (closest)?
Buy the box. Its certain payoff is $20, worth about $19.22 today at a 4% rate, but it trades at $18.00. Buying the cheap box locks in a present value gain of roughly $1.2, closest to $1.30.
- ABuy the box; PV profit about $0.70
- BSell the box; PV profit about $0.70Correct
- CSell the box; PV profit about $2.00
- DBuy the box; PV profit about $1.30
Explanation
Fair value = 20 × e^(-0.04) = 19.215... Check: e^(-0.04)=0.96079, so 19.216. The quote of 18.00 is below fair value, so the box is cheap: buy it, receiving a certain 20 for 18, PV profit 1.22. Re-check options: the closest is buy, about 1.30? Profit = 19.216 - 18 = 1.216, nearest to 1.30.
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