Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Simple Stochastic Rate Model for Rate Equity Hybrid Products

A Simple Stochastic Rate Model for Rate Equity Hybrid Products AbstractA positive spot rate model driven by a gamma process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent processes, a gamma process, a variance gamma process and a Wiener integral with respect to the Dirichlet process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk, 14(1), pp. 95–122). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

A Simple Stochastic Rate Model for Rate Equity Hybrid Products

Download PDF

A Simple Stochastic Rate Model for Rate Equity Hybrid Products

Abstract

AbstractA positive spot rate model driven by a gamma process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent processes, a gamma process, a variance gamma process and a Wiener integral with respect to the Dirichlet process. The generalized Stieltjes...
Loading next page...
 
/lp/taylor-francis/a-simple-stochastic-rate-model-for-rate-equity-hybrid-products-w3YN8mbmRQ
Publisher
Taylor & Francis
Copyright
© Taylor and Francis Group, LLC
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2013.770240
Publisher site
See Article on Publisher Site

Abstract

AbstractA positive spot rate model driven by a gamma process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent processes, a gamma process, a variance gamma process and a Wiener integral with respect to the Dirichlet process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk, 14(1), pp. 95–122).

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Nov 1, 2013

Keywords: Exponential Lévy models; short rate; rate equity hybrid products; large step simulation; quantization

References

  • Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion)
  • Bond and option pricing when short rates are lognormal
  • The market model of interest rate dynamics
  • Option valuation using the fast Fourier transform
  • Markets, profits, capital, leverage and returns
  • Markets as a counterparty: an introduction to conic finance
  • Some new results for Dirichlet processes
  • Distribution functions of means of a Dirichlet process
  • A theory of the term structure of interest rates
  • The Lévy Libor model
  • Term structure models driven by general Lévy processes
  • Change of numéraire, changes of probability measures and pricing of options
  • Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation
  • Dirichlet mean identities and laws of a class of subordinators
  • An exact bond option pricing formula
  • Least squares quantization in PCM
  • The variance gamma process and option pricing
  • The variance gamma (V.G.) model for share market returns
  • Structured products equilibria in conic two price markets. Working Paper, Robert H
  • Optimal quantization methods and applications to numerical problems in finance
  • The generalized Stieltjes transform and its inverse
  • Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures
  • An equilibrium characterisation of the term structure