FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A European put on a non-dividend-paying stock has K = 50, T = 0.5 years and a continuously compounded risk-free rate of 4%. The model gives N(-d2) = 0.40, and e^(-0.02) = 0.9802. What is the approximate change in the put price for a one percentage point increase in the risk-free rate?
The put price falls by about 0.098. Put rho is minus K times T times e^(-rT) times N(-d2), which is -50 × 0.5 × 0.9802 × 0.40 = -9.80 per unit rate change, or about -0.098 for a one percentage point rise.
- A-0.098Correct
- B+0.098
- C-0.245
- D-0.500
Explanation
Put rho = -K T e^(-rT) N(-d2) = -50 × 0.5 × 0.9802 × 0.40 = -9.80 per 1.00 change in rate. For a 0.01 change the put price falls by about 0.098. +0.098 has the wrong sign. -0.245 omits N(-d2).
Did you get it right without looking?
One question tells you little. A timed set on Option Sensitivity Measures: The "Greeks" shows your real accuracy, how long you take and where you lose marks.
More Option Sensitivity Measures: The "Greeks" questions
- A trader holds a long position in a European call option on a non-dividend-paying stock. Holding all else constant, which statement about th…
- Holding other inputs constant, for which European option is gamma generally greatest?
- A risk manager compares two long option positions on the same stock with the same strike: Option A expires in one week and Option B in one y…
- A delta-neutral portfolio has a gamma of -2,400 (change in portfolio delta per $1 move in the stock). The stock price rises suddenly by $2. …
- A trader holds a long position in 10,000 European call options on a non-dividend-paying stock. Each call has a delta of 0.55. To make the po…
- A call option has delta 0.60 and gamma 0.04 per dollar. The stock rises by 2 dollars. Using a delta-gamma approximation, what is the approxi…