This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the
theory and applications of path integrals. It is the first book to explicitly solve path integrals of …

Praise for The Volatility Surface" I'm thrilled by the appearance of Jim Gatheral's new book
The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

We study the Heston model, where the stock price dynamics is governed by a geometrical
(multiplicative) Brownian motion with stochastic variance. We solve the corresponding …

After the celebrated Black--Scholes formula for pricing call options under constant volatility,
the need for more general nonconstant volatility models in financial mathematics motivated …

Using the multifractional Brownian motion as a model of the price dynamics, we analyze the
impact of the COVID-19 pandemic on the efficiency of fifteen financial markets from Europe …

We treat the problem of option pricing under a stochastic volatility model that exhibits long-
range dependence. We model the price process as a Geometric Brownian Motion with …

We derive an asymptotic expansion formula for option implied volatility under a two-factor
jump-diffusion stochastic volatility model when time-to-maturity is small. We further propose …

The literature on volatility modelling and option pricing is a large and diverse area due to its
importance and applications. This paper provides a review of the most significant volatility …

We consider the pricing and hedging problem for options on stocks whose volatility is a
random process. Traditional approaches, such as that of Hull & White, have been successful …