## Abstract

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.

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.

Originalsprache | Englisch |
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Publikationsstatus | Veröffentlicht - 1 Sept. 2009 |