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Option Pricing with Transaction Costs and Stochastic Interest Rate

Option Pricing with Transaction Costs and Stochastic Interest Rate AbstractIn the case when transaction costs are associated with trading assets the option pricing problem is known to lead to solving nonlinear partial differential equations even when the underlying asset is modelled using a simple geometric Brownian motion. The nonlinear term in the resulting PDE corresponds to the presence of transaction costs. We generalize this model to a stochastic one-factor interest rate model. We show that the model follows a nonlinear parabolic type partial differential equation. Under certain assumption we prove the existence of classical solution for this model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Option Pricing with Transaction Costs and Stochastic Interest Rate

SenGupta, Indranil
Applied Mathematical Finance , Volume 21 (5): 18 – Sep 3, 2014
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Option Pricing with Transaction Costs and Stochastic Interest Rate

SenGupta, Indranil
Applied Mathematical Finance , Volume 21 (5): 18 – Sep 3, 2014

Abstract

AbstractIn the case when transaction costs are associated with trading assets the option pricing problem is known to lead to solving nonlinear partial differential equations even when the underlying asset is modelled using a simple geometric Brownian motion. The nonlinear term in the resulting PDE corresponds to the presence of transaction costs. We generalize this model to a stochastic one-factor interest rate model. We show that the model follows a nonlinear parabolic type partial differential equation. Under certain assumption we prove the existence of classical solution for this model.

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Publisher
Taylor & Francis
Copyright
© 2014 Taylor & Francis
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2014.881263
Publisher site
See Article on Publisher Site

Abstract

AbstractIn the case when transaction costs are associated with trading assets the option pricing problem is known to lead to solving nonlinear partial differential equations even when the underlying asset is modelled using a simple geometric Brownian motion. The nonlinear term in the resulting PDE corresponds to the presence of transaction costs. We generalize this model to a stochastic one-factor interest rate model. We show that the model follows a nonlinear parabolic type partial differential equation. Under certain assumption we prove the existence of classical solution for this model.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Sep 3, 2014

Keywords: Stochastic interest rate; parabolic PDE; transaction costs; option pricing; classical solution

References

  • The pricing of options and corporate liabilities
  • Option replication in discrete time with transaction costs
  • A theory of term structure of interest rates
  • European option pricing with transaction costs
  • Path-dependent options and transaction costs, philosophical transactions
  • Term structure movements and pricing interest rate contingent claims
  • Optimal replication of contingent claims under transaction costs
  • Hedging option portfolios in the presence of transaction costs
  • Pricing interest rate derivative securities
  • On Leland’s strategy of option pricing with transaction costs
  • Option pricing and replication with transaction costs
  • Numerical solutions for option pricing models including transaction costs and stochastic volatility
  • Solutions to a gradient-dependent integrodifferential parabolic problem arising in the pricing of financial options in a Lévy market
  • An equilibrium characterization of the term structure
  • An asymptotic analysis of an optimal hedging model for option pricing with transaction costs
  • A uniqueness theorem for a class of non-classical parabolic equations