A Unified Market Model for Swaptions and Constant Maturity Swaps

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.