The Heston Model with Time-Dependent Correlation Driven by Isospectral Flows

Abstract

In this work, we extend the Heston stochastic volatility model by including a time-dependent correlation that is driven by isospectral flows instead of a constant correlation, being motivated by the fact that the correlation between, e.g., financial products and financial institutions is hardly a fixed constant. We apply different numerical methods, including the method for backward stochastic differential equations (BSDEs) for a fast computation of the extended Heston model. An example of calibration to market data illustrates that our extended Heston model can provide a better volatility smile than the Heston model with other considered extensions.

Keywords

• correlation flow
• isospectral flow
• the Heston stochastic volatility
• backward stochastic differential equation
• time-dependent correlation