Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Explanation:

Explanation

This question describes the bisection method for finding implied volatility:

Initial bounds: 0% (gives price < market price) and 30% (gives price > market price)
First iteration: Average = 15% → gives price still lower than market price

In the bisection method:

When the calculated price is lower than the market price, the true implied volatility must be higher than the current estimate
When the calculated price is higher than the market price, the true implied volatility must be lower than the current estimate

Current situation:

15% gives price < market price → True IV > 15%
Therefore, we need to replace the lower bound (0%) with 15% and keep the upper bound (30%)
New range: 15% to 30%
New average: (15% + 30%)/2 = 22.5%

This corresponds to Option B: "Replace 0% with 15%, recalculate the averaged volatility using 30% and 15%, use the new average to compute the option price using the BSM formula, and compare it with the market price."

The bisection method continues iteratively narrowing the range until the calculated price converges to the market price.

Explanation:

Explanation

This question describes the bisection method for finding implied volatility:

Initial bounds: 0% (gives price < market price) and 30% (gives price > market price)
First iteration: Average = 15% → gives price still lower than market price

In the bisection method:

When the calculated price is lower than the market price, the true implied volatility must be higher than the current estimate
When the calculated price is higher than the market price, the true implied volatility must be lower than the current estimate

Current situation:

15% gives price < market price → True IV > 15%
Therefore, we need to replace the lower bound (0%) with 15% and keep the upper bound (30%)
New range: 15% to 30%
New average: (15% + 30%)/2 = 22.5%

The bisection method continues iteratively narrowing the range until the calculated price converges to the market price.

Comments (0)

No comments yet.

Q-47. Jasmine Tang, FRM, is using a simple method called "successive bisection" to determine the implied volatility of a traded option. Jasmine starts with a volatility of zero (this gives a BSM price that is less than the option market price) and a volatility of 30% (this gives a BSM price that is higher than the option market price). She then takes the average of these two volatilities, i.e., 15%, as the new volatility and uses it to compute the option price using the BSM formula. The revised option price is now much closer to the market price but still a bit low. Which of the following statements correctly describes the next step that Jasmine should perform?

Exam-Like

Replace 30% with 15%, recalculate the averaged volatility using 0% and 15%, use the new average to compute the option price using the BSM formula, and compare it with the market price.

50.0%

Replace 0% with 15%, recalculate the averaged volatility using 30% and 15%, use the new average to compute the option price using the BSM formula, and compare it with the market price.

50.0%

Treat 15% as a rough estimate of the implied volatility, because the revised option price is now much closer to the market price.

Shift to a procedure that are more numerically efficient, which involves solving a nonlinear equation.