[DRAFT] Interest Rate Swap Modeling
Table of Contents
Stochastic Volatility with Regime-Switching
The Cox-Ingersoll-Ross (CIR) model with regime-switching captures the impact of shifting economic conditions on interest rate volatility:
where
Interest Rate Swap Discounting and Forward Rates
The price
where
Multivariate Markov-switching GARCH for Spread and Volatility Modeling
For spread and volatility modeling in IRS, a Multivariate Markov-switching GARCH (MSGARCH) model is used, particularly when IRS rates correlate with other rates such as LIBOR:
where
IRS Valuation Using the Hybrid Model
The present value
where
Future Research Directions
Future research could explore machine learning integration to dynamically select regime parameters and high-frequency data analysis to capture intraday volatility in IRS markets, aligning valuation tools with rapid market shifts.
References
Jiling Cao, Teh Raihana Nazirah Roslan, and Wenjun Zhang. (2018). Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching. Methodology and Computing in Applied Probability, 20(4), 1359–1379. https://doi.org/10.1007/s11009-018-9624-5
John Hull and Alan White. (2014). OIS Discounting, Interest Rate Derivatives, and the Modeling of Stochastic Interest Rate Spreads. Journal of Investment Management. https://ssrn.com/abstract=2359610