A Unified Market Model for Swaptions and Constant Maturity Swaps
International Journal of Theoretical and Applied Finance, Vol. 24, No. 4, 2021, https://doi.org/10.1142/S0219024921500266
38 Pages Posted: 24 Aug 2019 Last revised: 24 Feb 2022
Date Written: August 20, 2019
Abstract
Internal-rate-of-return (IRR) settled swaptions are the main interest rate volatility instruments in the European interest rate markets. Industry practice is to use an approximation formula to price IRR swaptions based on Black model, which is not arbitrage-free. We formulate a unified market model to incorporate both swaptions and constant maturity swaps (CMS) pricing under a single, self-consistent framework. We demonstrate that the model is able to calibrate to market quotes well, and is also able to efficiently price both IRR-settled and swap-settled swaptions, along with CMS products. We use the model to illustrate the difference in implied volatilities for IRR-settled payer and receiver swaptions, the pricing of zero-wide collars and in-the-money (ITM) swaptions, the implication on put-call parity, and the issue of negative vega. These findings offer important insights to the ongoing reform in the European swaption market.
Keywords: interest rate market, swaptions, constant maturity swaps, derivative valuation, stochastic volatility models, fixed income market, interest rate models
JEL Classification: G13
Suggested Citation: Suggested Citation