FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A European call on a non-dividend-paying stock trades at a market price of 6.20. Using a volatility of 20% in the Black-Scholes-Merton model gives a price of 5.80, and using 25% gives 7.10. Vega is positive and the price is roughly linear in volatility over this range. Which is the best estimate of implied volatility?
The implied volatility is about 21.5%. Interpolating linearly, the market price lies 0.4 of the 1.3 price gap above the 20% price, which is 30.8% of the 5-point volatility range, adding about 1.54 points to 20%.
- A21.5%Correct
- B22.7%
- C23.1%
- D24.0%
Explanation
Linear interpolation: (6.20-5.80)/(7.10-5.80)=0.4/1.3=0.3077. Multiply by 5% gives 1.54%. Implied volatility is about 21.54%. Choosing 22.7% or 23.1% overstates the fraction.
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