# Quadratic approximation of slow factor of volatility in a Multi-factor Stochastic volatility Model

## TL;DR

This paper introduces a multifactor stochastic volatility model where the slow volatility factor is approximated by a quadratic arc, using perturbation techniques to derive approximate European option prices.

## Contribution

The paper presents a novel approximation of the slow volatility factor with a quadratic arc and derives a modified Black-Scholes framework for pricing.

## Key findings

- Derived a simplified European option pricing formula
- Expressed the modified price in terms of Black-Scholes price
- Provided a perturbation-based approximation method

## Abstract

In the present work, we propose a new multifactor stochastic volatility model in which slow factor of volatility is approximated by a parabolic arc. We retain ourselves to the perturbation technique to obtain approximate expression for European option prices. We introduce the notion of modified Black-Scholes price. We obtain a simplified expression for European option price which is perturbed around the modified Black-Scholes price and have also obtained the expression of modified price in terms of Black-Scholes price.