Implied volatility formula of European Power Option Pricing

TL;DR

This paper derives a new implied volatility estimation formula for European power options with specific payoff functions, extending traditional models and validating with Monte Carlo simulations.

Contribution

It introduces a generalized implied volatility formula for European power options using quadratic Taylor approximations, expanding on previous models.

Findings

Derived explicit implied volatility formulas for power options

Extended traditional implied volatility models to power options

Validated formulas with Monte Carlo simulations

Abstract

We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of $V=(S^{\alpha}_T-K)^{+}$ and $V=(S^{\alpha}_T-K^{\alpha})^{+}$ ($\alpha>0$)respectively. Using quadratic Taylor approximations, We develop the computing formula of implied volatility in European power call option and extend the traditional implied volatility formula of Charles J.Corrado, et al (1996) to general power option pricing. And the Monte-Carlo simulations are also given.