The Co-Terminal Swap Market Model with Bergomi Stochastic Volatility

TL;DR

This paper introduces a co-terminal swap market model based on Bergomi's stochastic volatility framework, enabling straightforward PnL analysis and enhanced control over interest rate derivative positions without complex calibration.

Contribution

It extends the forward variance modeling approach to interest rate markets, providing a flexible, calibration-free model for better exotic product management.

Findings

Model simplifies PnL analysis and understanding.

High flexibility in controlling model dynamics.

Numerical experiments demonstrate effectiveness for Bermudan swaptions.

Abstract

In this article, we apply the forward variance modeling approach by L.Bergomi to the co-terminal swap market model. We build an interest rate model for which all the market price changes of hedging instruments, interest rate swaps and European swaptions, are interpreted as the state variable variations, and no diffusion parameter calibration procedure is required. The model provides quite simple profit and loss (PnL) formula, with which we can easily understand where a material PnL trend comes from when it appears, and consider how we should modify the model parameters. The model has high flexibility to control the model dynamics because parameter calibration is unnecessary and the model parameters can be used solely for the purpose of the model dynamics control. With the model, the position management of the exotic interest rate products, e.g. Bermudan swaptions, can be carried out in a more sophisticated and systematic manner. A numerical experiment is performed to show the effectiveness of the approach for a Canary swaption, which is a special form of a Bermudan swaption.