Path Dependent Option Pricing: The Path Integral Partial Averaging Method

  title={Path Dependent Option Pricing: The Path Integral Partial Averaging Method},
  author={Andrew Matacz},
  journal={Derivatives eJournal},
  • 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… 

Efficient option pricing with path integral

It is shown how the path integral approach can be worked out in order to obtain fast and accurate predictions for the value of a large class of options, including those with path-dependent and early exercise features.

Pricing exotic options in a path integral approach

A general formula to price European path-dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms, which exhibits competitive performances when pricing at-the-money and out-of- the-money options.

Path Integral and Asian Options

In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path

Path integral and asset pricing

We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path

Option pricing in a path integral framework

This dissertation is an examination of methods for computing an option price using a path integral framework based on the Black and Scholes paradigm, and a similar approach using normalised Hermite orthogonal polynomials is presented.

A Path Integral Approach to Asset-Liability Management

Evaluation of Point Barrier Options in a Path Integral Framework Using Fourier-Hermite Expansions

The pricing of point barrier or discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. In this paper we develop a



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.

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.

High-accuracy discrete path integral solutions for stochastic processes with noninvertible diffusion matrices. II. Numerical evaluation

A remarkable property of the symmetric Trotter splitting is used to systematically eliminate the lower-order errors resulting from time discretization, leading to a significant reduction of the number of time steps that are required to retain a given accuracy for a given net increment t=Nτ, and significantly increasing the feasibility of path integral calculations.