FRM Part I · FRM Exam Part I · Properties of Options
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%. The stock pays no dividends. Using the lower bound c >= S0 - K*exp(-rT), what is the lower bound for the call price (nearest cent)?
The lower bound is 3.88. For a non-dividend-paying stock, the call must be worth at least the stock price minus the present value of the strike. Discounting 48 at 4% for one year gives 46.12, and 50 minus 46.12 equals 3.88, above the 2.00 intrinsic value.
- A2.00
- B3.88Correct
- C4.00
- D1.88
Explanation
Present value of strike = 48*exp(-0.04) = 48*0.960789 = 46.118. Lower bound = 50 - 46.118 = 3.88. Using 2.00 ignores discounting of the strike (intrinsic value). 4.00 uses the wrong sign (exp(+rT) effects approximated). 1.88 subtracts the discounted value incorrectly.
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 portfolio manager holds a stock at $100 and buys a 1-year European put with strike $95 for $4, financed by selling a 1-year European call …
- A stock trades at $80 and will pay a single dividend of $3 just before the ex-dividend date in 3 months. An American call on this stock has …
- An investor buys a share at $100, buys a European put with strike $95 for $3, and writes a European call with strike $110 for $2, all with t…
- A non-dividend-paying stock trades at 50. A European put with strike 55 expires in 1 year, and the continuously compounded risk-free rate is…
- An investor buys a European put option on a stock with a strike price of $50 and pays a premium of $3.20. At expiration the stock trades at …
- European options on a non-dividend-paying asset expire in 6 months. The continuously compounded risk-free rate is 4%. Prices are: call strik…