FRM Part I · FRM Exam Part I · Options Markets
A non-dividend-paying stock trades at $50. A European call with strike $50 and six months to expiry is priced at $4.00. The continuously compounded risk-free rate is 4% per year. What is the no-arbitrage price of a European put with the same strike and maturity? (e^-0.02 = 0.980199)
Using put-call parity, the put equals the call plus the present value of the strike minus the stock price: 4.00 + 49.01 - 50 = about $3.01, so the closest answer is $3.02. Skipping the discounting of the strike would wrongly give $4.00.
- A$2.02
- B$3.02Correct
- C$4.00
- D$5.02
Explanation
Put-call parity: p = c + K e^{-rT} - S0 = 4.00 + 50(0.980199) - 50 = 4.00 + 49.01 - 50 = 3.01, about $3.02 given rounding of 49.0100 (4+49.00995-50 = 3.00995, so $3.01). Closest option is $3.02. Ignoring discounting would give $4.00 (wrong base). Adding S0 instead of subtracting gives $5.02-type errors.
Did you get it right without looking?
One question tells you little. A timed set on Options Markets shows your real accuracy, how long you take and where you lose marks.
More Options Markets questions
- An investor buys a call with strike $30 for $4, sells a call with strike $35 for $2, and both expire in the same month. Which describes the …
- A portfolio manager holds a stock at $100 and buys a 1-year European put with strike $95 for $4, financing it by selling a 1-year European c…
- A trader constructs a bull spread using calls: buys a call with strike $30 for $4 and writes a call with strike $35 for $1.50. Which stateme…
- Which statement about an option's intrinsic value and time value is correct for a European-style call option that is currently out of the mo…
- An investor buys a European put on a non-dividend stock with strike $45 for a premium of $2.50. At expiry the stock price is $41. What is th…
- A stock trades at USD 100. An investor holds the stock and buys a European put with strike USD 95 for USD 2.00, financed by selling a Europe…