Answer-first summary for fast verification
Answer: 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.
## Explanation In the successive bisection method for finding implied volatility: - We start with two volatility bounds: one that gives a price **below** the market price (0% volatility) and one that gives a price **above** the market price (30% volatility) - We calculate the midpoint (15% volatility) - The new midpoint gives a price that is **still below** the market price - Since the new price is below market price, we need to **replace the lower bound** (0%) with the midpoint (15%) - This maintains the bracket where: - Lower bound (15%) gives price < market price - Upper bound (30%) gives price > market price - We then recalculate the average using 15% and 30% to get a new midpoint (22.5%) This is the correct bisection procedure: always replace the bound that maintains the bracket where the true implied volatility lies between the two bounds. **Option A** is incorrect because it would replace the upper bound, which would break the bracket since both bounds would then give prices below market price. **Option C** is incorrect because 15% is not the final answer - the price is still "a bit low" so we need to continue iterating. **Option D** is incorrect because successive bisection is a valid numerical method and we should continue with it until we achieve the desired precision.
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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?
A
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.
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.
C
Treat 15% as a rough estimate of the implied volatility, because the revised option price is now much closer to the market price.
D
Shift to a procedure that are more numerically efficient, which involves solving a nonlinear equation.