Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy

Büttler, Hans-Jürg

doi:10.2307/2235497

Cited by 17 publications

(14 citation statements)

References 40 publications

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“…Most of these methods exploit the specific structure of the Bellman equation and thus are not suitable for our problem. For example, Büttler (1995) and Candler (1999) apply finite differences to solve the Bellman equation as a partial differential equation (PDE). However, finite differences cannot be used to solve our functional differential equation.…”

Section: Global Approximation Techniquesmentioning

confidence: 99%

Numerical solution of dynamic equilibrium models under Poisson uncertainty

Posch

Trimborn

2013

Journal of Economic Dynamics and Control

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households. Terms of use: Documents inJEL-Code: C630, E210, O410.

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Section: Global Approximation Techniquesmentioning

confidence: 99%

Numerical solution of dynamic equilibrium models under Poisson uncertainty

Posch

Trimborn

2013

Journal of Economic Dynamics and Control

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“…Büttler (1995) observed that the numerical accuracy of the bond price computed depends sensibly on the choice of the boundary-approximation scheme applied at r ϭ r min . The prescription of an inaccurate numerical-boundary condition would deteriorate the overall accuracy of the numerical solutions at interior node points.…”

Section: Bond Price Calculationsmentioning

confidence: 99%

Accuracy and Reliability Considerations of Option Pricing Algorithms

Kwok

Lau

2001

Journal of Futures Markets

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A wide variety of computational schemes have been proposed for the numerical valuation of various classes of options. Experiences in numerical computation have revealed that the details of the implementation of the auxiliary conditions in the numerical algorithms may have profound effects on numerical accuracy. Difficulties in designing algorithms that deal with the path-dependent payoffs, monitoring features, etc., have been well reported in the literature. In this article, the theoretical issues on the assessment of numerical schemes with regard to accuracy of approximation of auxiliary conditions, rate of convergence, and oscillation phenomena are reviewed. In particular, the oscillation phenomena in bond-price calculations and the intricacies in implementing the auxiliary conditions in barrier options, proportional step options, and lookback options are discussed. With different types of options and modes of monitoring (continuous or discrete), the optimal method of placing the lattice nodes with reference to

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“…Since it is very difficult to analytically solve this PDE, some different discretizations and different numerical methods have been proposed. Büttler in [2] (1995) applied finite difference method to find the evaluation of callable bonds. Büttler and Waldvogel in [3] (1996) derived an analytic expression for the Green's function of the corresponding PDE for certain specific interest rate models, and developed a semi-analytic method for pricing callable bonds with notice.…”

Section: Introductionmentioning

confidence: 99%

Pricing Callable Bonds Based on Monte Carlo Simulation Techniques

Ding¹,

Fu²,

So³

2012

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In this paper, a Monte Carlo method, which is based on some new simulation techniques proposed recently, is presented to numerically price the callable bond with several call dates and notice under the Cox-Ingersoll-Ross (CIR) interest rate model. The corresponding algorithms are also presented to practical callable bond pricing. The numerical experiments show that this method works very well for callable bond under the CIR interest rate model.

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Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy

Cited by 17 publications

References 40 publications

Numerical solution of dynamic equilibrium models under Poisson uncertainty

Numerical solution of dynamic equilibrium models under Poisson uncertainty

Accuracy and Reliability Considerations of Option Pricing Algorithms

Pricing Callable Bonds Based on Monte Carlo Simulation Techniques

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