Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
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Beáta Stehlíková
Abstract
We deal with the interest rate model proposed by Schaefer and Schwartz, which models the long rate and the spread, defined as the difference between the short and the long rates. The approximate analytical formula for the bond prices suggested by the authors requires a computation of a certain constant, defined via a nonlinear equation and an integral of a solution to a system of ordinary differential equations. A quantity entering the nonlinear equation is expressed in a closed form, but it contains infinite sums and evaluations of special functions. In this paper we use perturbation methods to compute the constant of interest as an asymptotic serie with coefficients given in closed form and expressed using elementary functions. A quick computation of the bond prices, which our approach allows, is essential for example in calibration of the model by means of fitting the observed yields, where the theoretical bond prices need to be recalculated for every observed date and maturity, as well as every combination of parameters considered. The first step of our derivation is identification of a small parameter in the problem, since it is not immediately clear. We verify our choice by numerical experiments using the values of parameters from the literature.
This work was supported by by VEGA 1/0251/16 grant.
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© 2018 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Small-large subgroups of the reals
- Structural properties of algebras of S-probabilities
- Approximation in quantum measure spaces
- On Fibonomial sums identities with special sign functions: analytically q-calculus approach
- On the proximity of multiplicative functions to the number of distinct prime factors function
- Truncated euler polynomials
- Growth series of crossed and two-sided crossed products of cyclic groups
- Weakly U-abundant semigroups with strong Ehresmann transversals
- Iterative learning control with pulse compensation for fractional differential systems
- Rectifiable and nonrectifiable solution curves of half-linear differential systems
- Uniqueness properties of meromorphic functions in the light of three shared sets
- A new family of analytic functions defined by means of Rodrigues type formula
- Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
- On the solutions of a second-order difference equation in terms of generalized Padovan sequences
- Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
- A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation
- Productively sequential spaces
- Euler classes of vector bundles over iterated suspensions of real projective spaces
- The stationary distribution and ergodicity of a stochastic mutualism model
- Restricted injective dimensions over local homomorphisms
