An upwind numerical approach for an American and European option pricing model
Applied Mathematics and Computation
Convex analysis and variational problems
Convex analysis and variational problems
Far Field Boundary Conditions for Black--Scholes Equations
SIAM Journal on Numerical Analysis
A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion
SIAM Journal on Scientific Computing
An adaptive extrapolation discontinuous Galerkin method for the valuation of Asian options
Journal of Computational and Applied Mathematics
A numerical method for pricing spread options on LIBOR rates with a PDE model
Mathematical and Computer Modelling: An International Journal
A characteristics-finite differences method for the Hobson-Rogers uncertain volatility model
Mathematical and Computer Modelling: An International Journal
Pricing of early-exercise Asian options under Lévy processes based on Fourier cosine expansions
Applied Numerical Mathematics
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Asian options prices can be modelled in the Black-Scholes framework leading to two-factor models depending on the asset price, the average of the asset price and the time. They can also involve inequality constraints, as in the case of Amerasian options, leading to variational inequalities (VI). In the first section, we completely describe the pricing model for fixed-strike Eurasian and Amerasian options and list some properties satisfied by the option value function. Then, since no solutions in closed form are known, we deal with the numerical solution of the above problems proposing a general methodology: an iterative algorithm for the VI, combined with higher order Lagrange-Galerkin methods for partial differential equations. Finally, numerical results are shown.