# Path integral approach to Asian options in the Black-Scholes model

@article{Devreese2010PathIA, title={Path integral approach to Asian options in the Black-Scholes model}, author={Jeroen P. A. Devreese and Damiaan Lemmens and Jacques Tempere}, journal={Physica A-statistical Mechanics and Its Applications}, year={2010}, volume={389}, pages={780-788} }

We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is… Expand

#### 22 Citations

Path integral pricing of outside barrier Asian options

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Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent… Expand

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In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive… Expand

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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… Expand

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From the analysis of real data, the best value for q is identified which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to the model. Expand

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The MCMC method is developed by discretizing the path integral on a time lattice and evaluating this discretized form for various scenarios, with particular attention paid to the existence of autocorrelations, their decay with the number of sweeps, and the resulting estimate of the corresponding errors. Expand

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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… Expand

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