Option Pricing With Volatility of Volatility: A Simple, Closed-Form Formula

Abstract

This is the first paper to provide a simple, explicit formula (that doesn’t require
numerical/computational methods) under stochastic volatility. The formula
is as simple as the classical Black-Scholes pricing formula. Furthermore,
this paper modifies the Black-Scholes model to make it consistent with the
empirical reality. Moreover, it is the first paper to show that the option price
depends on the volatility of the volatility using the classical Black-Scholes
framework.

Keywords: option pricing, stochastic volatility, closed-form solution, Black-Scholes PDE, volatility of volatility

JEL Classification: G0, C0, C5