FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A stock follows geometric Brownian motion with expected return μ = 11% per year and volatility σ = 20% per year. What is the expected continuously compounded (log) return per year, ln(S_T/S_0)/T in expectation?
The expected continuously compounded return equals the drift minus half the variance: 11% − 0.5 × (0.20)² = 11% − 2% = 9% per year. Using 11% ignores the Ito adjustment that arises because the price is lognormal.
- A11%
- B9%Correct
- C13%
- D10%
Explanation
The expected log return is μ − σ²/2 = 0.11 − 0.04/2 = 0.11 − 0.02 = 0.09, or 9%. Using 11% ignores the Ito convexity adjustment. Adding the adjustment (13%) has the wrong sign.
Did you get it right without looking?
One question tells you little. A timed set on The Black-Scholes-Merton Model shows your real accuracy, how long you take and where you lose marks.
More The Black-Scholes-Merton Model questions
- A listed company issues warrants to outside investors, each exercisable into one newly issued share. Compared with an otherwise identical ex…
- A non-dividend-paying stock trades at 100. A European call has strike 90 and one year to expiry, and the continuously compounded risk-free r…
- Which of the following is an assumption of the original Black-Scholes-Merton model for pricing a European option?
- A company has 4 million shares outstanding and has issued 1 million warrants, each exercisable into one new share at $30. Just before exerci…
- A stock follows geometric Brownian motion with expected return μ = 12% per year and volatility σ = 20% per year. Using the BSM lognormal mod…
- A bank prices a European call on euros with the dollar as the domestic currency. The USD risk-free rate is 4% and the EUR risk-free rate is …