FRM Part I · FRM Exam Part I · Properties of Options
A non-dividend-paying stock trades at $50. A European call option on the stock has a strike of $45 and expires in one year. The continuously compounded risk-free rate is 4%. What is the lower bound for the call price?
The lower bound is $6.76. It equals the stock price minus the present value of the strike: 50 minus 45 times e to the power of minus 0.04, which is 50 minus 43.24. Using the undiscounted strike would wrongly give $5.
- A$5.00
- B$6.76Correct
- C$5.00 less the present value of interest, i.e. $3.24
- D$0.00
Explanation
The lower bound for a European call on a non-dividend stock is max(S0 - K e^(-rT), 0). K e^(-0.04) = 45 x 0.960789 = 43.235. So the bound is 50 - 43.235 = 6.76. Using the undiscounted strike gives $5.00, which ignores the time value of money on the strike.
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