Some Results on Partial Differential Equations and Asian Options

By Emilio Barucci, Sergio Polidoro, V. Vespri. 2001

145 citations recorded by the source corpus.

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.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/1dc7506f6475c9f4b9b92dad722859f956c05c93

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Citations in the corpus

Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form (2006, background): “More specifically, the following linear equation S(2)∂SSV + f(S)∂MV − ∂tV = 0, S, t > 0, M ∈ R with either f(S) = log (S) or f(S) = S, arises in the Black & Scholes theory when considering the problem of the pricing Asian option (see [3]).”
Pointwise estimates for a class of non-homogeneous Kolmogorov equations (2008, background): “More specifically, the following linear KFP equation S(2)∂SS V + f (S)∂M V − ∂t V = 0, S, t > 0, M ∈ R with either f (S) = log S or f (S) = S, arises in the Black and Scholes theory when considering the problem of the pricing of Asian options (see [3]).”
Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations (2005, background): “Such an idea was exploited in [6] to compute the price of asian options.”
On the complete model with stochastic volatility by Hobson and Rogers (2004, background): “Then, as in the case of path-dependent contingent claims such as Asian or look-back options, the augmented PDE associated to the model is strongly degenerate and standard analytical and numerical techniques do not apply.”
A survey on the classical theory for Kolmogorov equation (2019, unknown): “, for instance, [11] [59]), where, for example the equation ∂tP + 1 2σ (2)S(2)∂(2) SP + (log S)∂AP + r(S∂SP − P ) = 0, S > 0, A, t ∈ R (1.”
THE MOSER'S ITERATIVE METHOD FOR A CLASS OF ULTRAPARABOLIC EQUATIONS (2004, methodology): “Thus, by using the fundamental solution of L0, we get the needed L p loc estimate of the solution.”
Explicit parametrix and local limit theorems for some degenerate diffusion processes (2008, unknown): “(y − x)+), see [5] and [26].”
Linear and nonlinear ultraparabolic equations of Kolmogorov type arising in diffusion theory and in finance (2002, background): “1) by means of an elementary change of variables (see [6], page 479).”
On a class of degenerate parabolic equations of Kolmogorov type (2005, background): “4) by means of an elementary change of variables (see [6], page 479).”