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Hybrid Lévy Models: Design and Computational Aspects

Hybrid Lévy Models: Design and Computational Aspects A hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. Dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. Using market quotes for liquidly traded assets we show that the hybrid approach can be successfully calibrated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Hybrid Lévy Models: Design and Computational Aspects

Eberlein, Ernst; Rudmann, Marcus
Applied Mathematical Finance , Volume 25 (5-6): 24 – Nov 2, 2018
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Hybrid Lévy Models: Design and Computational Aspects

Abstract

A hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest...
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Publisher
Taylor & Francis
Copyright
© 2018 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2018.1536523
Publisher site
See Article on Publisher Site

Abstract

A hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. Dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. Using market quotes for liquidly traded assets we show that the hybrid approach can be successfully calibrated.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Nov 2, 2018

Keywords: Hybrid models; time-inhomogeneous Lévy processes; interest rate derivatives; equity derivatives; hybrid derivatives

References

  • Forward Start Options under Stochastic Volatility and Stochastic Interest Rates
  • Pricing of Foreign Exchange Options under the Heston Stochastic Volatility Model and CIR Interest Rates
  • A Lévy Process-Based Framework for the Fair Valuation of Participating Life Insurance Contracts
  • Pricing and Capital Requirements for with Profit Contracts: Modelling Considerations
  • International Stock-Bond Correlations in a Simple Affine Asset Pricing Model
  • A Multiple-Curve Lévy Forward Rate Model in A Two-Price Economy
  • Analysis of Fourier Transform Valuation Formulas and Applications
  • Lévy Term Structure Models: No-Arbitrage and Completeness
  • Exact Pricing Formulae for Caps and Swaptions in a Lévy Term Structure Model
  • On Correlating Lévy Processes
  • A Simple Stochastic Rate Model for Rate Equity Hybrid Products
  • Term Structure Models Driven by General Lévy Processes
  • Changes of Numéraire, Changes of Probability Measure and Option Pricing
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  • Pricing Interest-Rate Derivative Securities
  • Stochastic Volatility with an Ornstein-Uhlenbeck Process: An Extension
  • The Stock-Bond Correlation and Its Implications for Asset Allocation