Articlegreen2001

SOME RESULTS ON PARTIAL DIFFERENTIAL EQUATIONS AND ASIAN OPTIONS

Emilio Barucci · Sergio Polidoro · Vincenzo Vesprı

139 citations0/0 files storedMathematical Models and Methods in Applied Sciences

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Differential Equations and Boundary Problems

Abstract

We analyze partial differential equations arising in the evaluation of Asian options. The equations are strongly degenerate partial differential equations in three dimensions. We show that the solution of the no-arbitrage partial differential equation is sufficiently regular and standard numerical methods can be employed to approximate it.

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References

1976The valuation of options for alternative stochastic processes 1990A pricing method for options based on average asset values 1993BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES 1995The value of an Asian option 1991A Quick Algorithm for Pricing European Average Options 1992Pricing European average rate currency options 1996PRICING OF AMERICAN PATH‐DEPENDENT CONTINGENT CLAIMS

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2010Density estimates for a random noise propagating through a chain of differential equations 2011Parametrix techniques and martingale problems for some degenerate Kolmogorov equations 2007Free boundary and optimal stopping problems for American Asian options 2004On the complete model with stochastic volatility by Hobson and Rogers 2005Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations 2012Approximations for Asian options in local volatility models 2016

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