FRM Part I · FRM Exam Part I · Trading Strategies
A bank issues a 3-year principal-protected note with a face value of USD 1,000 that returns the principal at maturity plus a participation in the rise of an equity index. The continuously compounded risk-free rate is 4% per year. Ignoring credit risk and fees, how much of the USD 1,000 can the bank spend on the option component (to the nearest dollar)?
The bank spends about USD 113 on options. The zero-coupon bond guaranteeing USD 1,000 costs 1,000 × e^(-0.12), about USD 887, and the remaining USD 113 of the proceeds is available to buy the equity-linked call option component.
- AUSD 113Correct
- BUSD 120
- CUSD 40
- DUSD 887
Explanation
The zero-coupon bond component costs 1,000 × e^(-0.04×3) = 1,000 × e^(-0.12) = 1,000 × 0.88692 = USD 886.92. The remainder, 1,000 − 886.92 = USD 113, funds the option. USD 120 simply multiplies 4% by 3 years without discounting the bond properly (undiscounted interest), and USD 887 is the bond cost, not the option budget.
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