What Are Stochastic Volatility Models For Option Pricing?

February 14, 2023

What Are Stochastic Volatility Models For Option Pricing?

Trading and Investing

Stochastic volatility models are a class of financial models used to value options and other financial derivatives. These models take into account the fact that the volatility of underlying assets, such as stocks or currencies, can change over time and that this change is itself unpredictable.

In a stochastic volatility model, the volatility of the underlying asset is modeled as a random variable that follows a stochastic process. Furthermore, the most commonly used stochastic process for modeling volatility is the Heston model, named after the economist Steven Heston. The Heston model assumes that the volatility of the underlying asset follows a mean-reverting process. Driven by a Brownian motion process.

Stochastic volatility models became used in option pricing. As a result, of their ability to more accurately capture the risk associated with changes in the volatility of the underlying asset. By incorporating the unpredictable nature of volatility changes into the pricing model. Stochastic volatility models can provide more accurate estimates of the fair value of options and other financial derivatives.

One of our favorite quant minds Professor Alex Lipton just announced a new paper with Adil Reghai: SPX, VIX and scale-invariant LSV.

Professor Lipton posted to Linkedin:

“Local Stochastic Volatility (LSV) models have become used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data. However, the literature misses a potent approach commonly used in physics and works with absolute (dimensional) variables rather than with relative (non-dimensional) ones.

While model parameters defined in absolute terms are counter-intuitive for trading desks and tend to be heavily time-dependent, relative parameters are intuitive and stable, making it easy to steer the model adequately and consistently with its Profit and Loss (PnL) explanation power. We propose a specification that first explores historical data and uses physically well-defined relative quantities to design the model. We then develop an efficient hybrid method to price derivatives under this specification. Furthermore, we also show how our method can become used for robust scenario generation purposes – an important risk management task vital for buy-side firms. These two figures below perfectly illustrate our point.”