DG method for numerical pricing of multi-asset Asian options – the case of options with floating strike. (English) Zbl 1458.91225

Hozman, Jiří; Tichý, Tomáš

Appl. Math., Praha 62, No. 2, 171-195 (2017).

Summary: Option pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts on two assets. Further, we focus only on one subclass – Asian options with floating strike – and introduce the concept of the dimensionality reduction with respect to the payoff leading to PDE with two spatial variables. Then the numerical option pricing scheme arising from the discontinuous Galerkin method is developed and some theoretical results are also mentioned. Finally, the aforementioned model is supplemented with numerical results on real market data.

MSC:

91G60	Numerical methods (including Monte Carlo methods)
91G20	Derivative securities (option pricing, hedging, etc.)
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q91	PDEs in connection with game theory, economics, social and behavioral sciences

Keywords:

option pricing; discontinuous Galerkin method; path-dependent option; basket option; floating strike

Software:

FreeFem++