An Empirical Analysis of Valuation Algorithms for Pricing Callable Snowball Floaters

In this paper we value a callable snowball floater, a complex interest rate instrument with variable coupon payments, which depend on the prevailing interest rates in arrears and recursively on previous coupon payments. The embedded option requires solving an optimal stopping problem using the dynamic programming principle. A well-known and widely used algorithm to estimate conditional expectations is a specific form of least squares Monte Carlo simulation introduced by Longstaff and Schwartz (2001), which we refer to as the LSM approach. Contrary to the standard approach, where discounted option values of the subsequent period are regressed on the current state variables, Longstaff and Schwartz (2001) use the ex post realized payoffs of in-the-money option scenarios from continuation instead. They argue that, in doing so, they get values less than or equal to the value implied by the optimal stopping rule, which provides an objective convergence criterion. We compare the LSM approach with the standard approach and use the price estimate from an elaborate nested Monte Carlo simulation as a benchmark. We empirically find that the LSM estimate of the embedded option might be considerably downward biased, whereas the standard estimate is much closer to the benchmark price. Moreover, we find that there is no optimal type of basis function that can generally be recommended for pricing interest rate instruments. Instead, we suggest using the LSM approach to determine the optimal type of basis function that results in the largest option value and rely on the standard approach to price the instrument. These are important issues to consider when pricing complex interest rate instruments, in general, and callable snowball floaters, in particular