Path Dependent Option Pricing: The Path Integral Partial Averaging Method

@article{Matacz1999PathDO,
  title={Path Dependent Option Pricing: The Path Integral Partial Averaging Method},
  author={Andrew Matacz},
  journal={Derivatives eJournal},
  year={1999}
}
  • A. Matacz
  • Published 1 November 1999
  • Mathematics
  • Derivatives eJournal
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one… 

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References

SHOWING 1-10 OF 59 REFERENCES

Using path integrals to price interest rate derivatives

We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (Black-Scholes type) partial differential equation and

A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods

The path integral Monte Carlo approach is applied to some specific financial problems: the pricing of a European option, a zero-coupon bond, a caplet, an American option, and a Bermudan swaption.

The Path Integral Approach to Financial Modeling and Options Pricing

In this paper we review some applications of the path integral methodology of quantum mechanics to financial modeling and options pricing. A path integral is defined as a limit of the sequence of

A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results

We use a path integral approach for solving the stochastic equations underlying the financial markets, and show the equivalence between the path integral and the usual SDE and PDE methods. We analyze

A path integral approach to option pricing with stochastic volatility : Some exact results

The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of

Pricing Continuous Asian Options: A Comparison of Monte Carlo and Laplace Transform Inversion Methods

In this paper, we investigate two numerical methods for pricing Asian options: Laplace transform inversion and Monte Carlo simulation. In attempting to numerically invert the Laplace transform of the

The Feynman–Kac Formula And Pricing Occupation Time Derivatives

In this paper, we undertake a study of occupation time derivatives that is derivatives for which the pay-off is contingent on both the terminal asset's price and one of its occupation times. To this

Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques

This paper considers the evaluation of derivative security prices within the Heath-Jarrow-Morton framework of stochastic interest rates, such as bond options. Within this framework, the stochastic

A fast algorithm for computing integrals in function spaces: Financial applications

A fast and general numerical algorithm for computing path integrals in function spaces and a number of financial applications of the algorithm are considered, including pricing European and American style interest rate options, path dependent options, and index amortization swaps.
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