FRM Part I · FRM Exam Part I · Properties of Options
A non-dividend-paying stock trades at 72. A European put on it has strike 80 and expires in six months. The continuously compounded risk-free rate is 5% per year. What is the lower bound for the put price?
The bound is the present value of the strike minus the stock price: 80e^(-0.025) - 72 = about 6.02. The strike is received only at expiry, so it must be discounted. The undiscounted intrinsic value of 8.00 overstates the bound for a European put.
- A6.02Correct
- B8.00
- C10.03
- D0.00
Explanation
The lower bound for a European put on a non-dividend stock is max(K e^(-rT) - S, 0). 80 x e^(-0.025) = 78.02, so the bound is 78.02 - 72 = 6.02. The figure 8.00 is the undiscounted intrinsic value, which is not a valid bound for a European put because the strike is received only at expiry. The 10.03 figure compounds the strike forward, which is the wrong sign on the rate.
Did you get it right without looking?
One question tells you little. A timed set on Properties of Options shows your real accuracy, how long you take and where you lose marks.
More Properties of Options questions
- A stock trades at 50. A European call on the stock has strike 48, expires in 1 year, and the continuously compounded risk-free rate is 4%. T…
- A European put has strike 40 and expires in two years. The continuously compounded risk-free rate is 6% per year. What is the highest price …
- Holding all other factors constant, which change would most clearly increase the value of a European call option on a non-dividend-paying st…
- A trader buys a European call with strike $60 for $5 and buys a European put with the same strike and expiry for $3 (a long straddle). Ignor…
- 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…
- A trader writes a European call with strike $80 for a premium of $4.50 and simultaneously buys the underlying stock at $78 (a covered call).…