CFA Level I · CFA Level I Exam · Pricing and Valuation of Options
A stock trades at 50. European options on it have a strike of 50 and one year to expiry. The annual risk-free rate is 4% (annual compounding), and the stock pays no dividends. The call is priced at 5.50. A trader builds a synthetic long put using the call, the stock, and a risk-free bond. The cost of this synthetic put is closest to:
The synthetic put costs about 3.58, closest to 3.54. It is built by buying the call, lending the present value of the strike (48.08) and shorting the stock: 5.50 + 48.08 - 50 = 3.58. Ignoring discounting would give 5.50.
- A3.54Correct
- B5.50
- C7.46
Explanation
Synthetic put = c + PV(X) - S = 5.50 + 50/1.04 - 50 = 5.50 + 48.08 - 50 = 3.58. Rounded, 3.58 is closest to 3.54 (the others are 5.50 and 7.46, far away). Using the undiscounted strike gives 5.50, and 7.46 comes from adding the stock instead of shorting it with PV mismatch.
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