FRM Part I · FRM Exam Part I · Properties of Options
A non-dividend-paying stock trades at 40. A European call with strike 38 and 1 year to expiry is being valued with a continuously compounded risk-free rate of 5%. What is the lower bound on the call's price (use exp(-0.05)=0.9512)?
The lower bound is the stock price minus the present value of the strike: 40 minus 38 times 0.9512, which is about 3.86. Using the undiscounted strike would give 2.00, ignoring the time value of money.
- A2.00
- B3.86Correct
- C4.14
- D40.00
Explanation
Lower bound = S0 - K*exp(-rT) = 40 - 38*0.9512 = 40 - 36.146 = 3.854, about 3.86 (rounding). The 2.00 option uses undiscounted strike (40-38), which is a wrong base. 4.14 would result from adding rather than subtracting a discount adjustment.
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