Valuation of Callable Range Accrual Linked to CMS Spread Under Generalized Swap Market Model

In this paper, we price a widely-used financial instrument, the callable range accrual linked to constant maturity swap (CMS) spread, with the least square Monte Carlo method (LSMC) under the generalized swap market model (GSMM). This method, based on the swap rate, does not only provide an intuitive pricing solution, but also captures the characteristics of the swap market, which helps market participants better face the challenge of the London interbank offered rate (LIBOR) phaseout. By choosing the prices valued by the two-factor Hull-White model in Bloomberg as a benchmark, our method provides an accurate result, following the economic intuitions. Last but not least, we examine the impacts from the shifting of the yield curve and volatility term structure by sensitivity analysis. We find that the price positively correlates with the volatility term structure among 1% shifts, while the relationship can be uncertain in larger shifts. The changes in the estimated parameters, such as the yield curve and volatility term structure, might reflect the occurrences of macroeconomic events, such as the COVID-19 pandemic.