A Payoff Consistent Approach to Cash-Settled Swaptions and CMS Replication

Publication Type

Conference Paper

Publication Date



European interest rate markets use cash-settlement (CS) for swaptions, the main interest rate volatility instrument. In the market only at-the-money (ATM) straddles and out-of-the-money (OTM) payers/receivers are liquidly quoted and usable as calibration instruments. As a result all ITM payer/receiver swaption prices are model-based. CS-swaptions form the basis for all volatility-sensitive interest rate product valuations such as constant maturity swaps (CMS), Bermudan swaptions and callable libor exotics. Therefore, mispricings of CS-swaptions impacts the whole spectrum of interest rate volatility products. As the difference between physical- and cash-settlement is often considered minor, a Black model based market-approximation (MA) formula is heavily used to value cash-settled swaptions across the industry. We show that at the forward swap rate (ATM) the value of cash-settled payer and receiver swaptions are economically significantly different, contrary to physical-settled swaptions. However, the MA formula implies equality for ATM payers/receivers. We will show that using the MA formula leads to economically significant mispricings of both ATM and ITM swaptions. Furthermore, we show problems in swaption portfolio risk management and significant mispricing of constant maturity swap (CMS) products using replication. This paper provides an overview of the market formula followed by a detailed analysis of the key reasons for valuation/sensitivity differences. We propose a stochastic volatility model to accurately capture the convex/concave payoff profile. The model is capable of accounting for the non-linear payoff profile while being analytically tractable. Furthermore, it has enough degree of freedom to be calibrated accurately to the implied volatility smile and skew in the swaption market. We report several key findings. The implied volatilities for cash-settled payer and receiver swaptions are shown to be different due to the convex and concave payoff profile. ITM swaptions can be valued effectively using the semi-analytical model formulated in this work, allowing for efficient risk management of large swaption portfolio. In addition, it is observed that vega for cash-settled payer swaptions could become negative in high interest rates scenarios. Finally, we detail the implications of these mispricings for CMS products.


Finance and Financial Management

Research Areas

Quantitative Finance


Bachelier Finance Society 8th World Congress 2014, June 2-6

City or Country

Brussels, Belgium

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