DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike

Jiří Hozman; Tomáš Tichý

Applications of Mathematics (2017)

  • Volume: 62, Issue: 2, page 171-195
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hozman, Jiří, and Tichý, Tomáš. "DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike." Applications of Mathematics 62.2 (2017): 171-195. <http://eudml.org/doc/287934>.

@article{Hozman2017,
abstract = {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.},
author = {Hozman, Jiří, Tichý, Tomáš},
journal = {Applications of Mathematics},
keywords = {option pricing; discontinuous Galerkin method; path-dependent option; basket option; floating strike},
language = {eng},
number = {2},
pages = {171-195},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike},
url = {http://eudml.org/doc/287934},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Hozman, Jiří
AU - Tichý, Tomáš
TI - DG method for numerical pricing of multi-asset Asian options—the case of options with floating strike
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 171
EP - 195
AB - 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.
LA - eng
KW - option pricing; discontinuous Galerkin method; path-dependent option; basket option; floating strike
UR - http://eudml.org/doc/287934
ER -

References

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