Numerical Methods for Finding Zeros of a Function

Geon Ho Choe
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Geon Ho Choe: Korea Advanced Institute of Science and Technology, Department of Mathematical Sciences

Chapter Chapter 16 in Quantitative Methods for Finance with Simulations II, 2026, pp 303-324 from Springer

Abstract: Abstract 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 ( σ ) = 0 $$f(\sigma )=0$$ in terms of an unknown variable σ $$\sigma $$ , 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-032-12331-2_16

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DOI: 10.1007/978-3-032-12331-2_16

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