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In this chapter we present numerical methods to find zeros of a function, which is used in computing the implied volatility. First, we construct an equation of the form \(f(\sigma )=0\) in terms of an unknown variable \(\sigma \) , and use a numerical method such as the bisection method, the secant method, the Newton method, or Halley’s method. Details in the application to option pricing will be given in the next chapter. The numerical methods for finding zeros presented here can also be used to compute the yield in bond pricing.

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Numerical Methods for Finding Zeros of a Function

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  • 发表日期：

    2026年

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  • Geon Ho Choe

摘要

In this chapter we present numerical methods to find zeros of a function, which is used in computing the implied volatility. First, we construct an equation of the form \(f(\sigma )=0\) in terms of an unknown variable \(\sigma \) , and use a numerical method such as the bisection method, the secant method, the Newton method, or Halley’s method. Details in the application to option pricing will be given in the next chapter. The numerical methods for finding zeros presented here can also be used to compute the yield in bond pricing.