TheVolatilitySurface

The book "The Volatility Surface: A Practitioner's Guide" by Jim Gatheral, published in 2006, is widely regarded as a key reference in the field of mathematical finance, specifically in the area of volatility modeling and option pricing.

The book covers various topics, including:

1. Implied volatility and its behavior across different strike prices and maturities.
2. Local volatility models, which estimate the instantaneous volatility at each point in time and price.
3. Stochastic volatility models, which incorporate the uncertainty in the volatility process itself.
4. The Heston model, a widely-used stochastic volatility model that allows for closed-form solutions for option prices.
5. The Sαβρ (Stochastic α, β, ρ) model, another popular stochastic volatility model, which is particularly useful for interest rate derivatives.
6. Volatility derivatives, such as variance swaps and volatility swaps, and their pricing.