Availability and accuracy of approximation formulas for CMS and CMS spread options

Determine whether accurate and readily applicable analytical or semi-analytical approximation formulas exist for pricing Constant Maturity Swap (CMS) options and CMS spread options, as alternatives to Monte Carlo simulation, and ascertain their adequacy for practical calibration and pricing tasks.

Background

The paper develops efficient GPU-accelerated Monte Carlo calibration techniques for several SABR/LIBOR market models and demonstrates their effectiveness on caplets and swaptions. For swaptions and more complex products, closed-form or simple approximation formulas are often unavailable, motivating the use of computationally intensive Monte Carlo methods.

In the conclusions, the authors note that extending calibration and pricing to more complex interest rate derivatives, such as CMS options and CMS spread options, raises the question of whether alternative approximation formulas to Monte Carlo are available and sufficiently accurate, highlighting an explicit uncertainty in the current literature.