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Digital Library of the
European Council for Modelling and Simulation |
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Title: |
Numerical Methods For Optimal Control Based Schemes For Volatility
Calibration And Algorithmic Trading |
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Authors: |
Deepak Kumar |
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Published in:
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(2011).ECMS
2011 Proceedings edited by: T. Burczynski, J. Kolodziej, A. Byrski, M. Carvalho. European Council for Modeling and Simulation. doi:10.7148/2011 ISBN:
978-0-9564944-2-9 25th
European Conference on Modelling and Simulation, Jubilee Conference Krakow,
June 7-10, 2011
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Citation
format: |
Kumar, D. (2011). Numerical
Methods For Optimal Control Based Schemes For Volatility Calibration And
Algorithmic Trading. ECMS 2011 Proceedings edited by: T. Burczynski,
J. Kolodziej, A. Byrski, M. Carvalho (pp. 289-295).
European Council for Modeling and Simulation. doi:10.7148/2011-0289-0295 |
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DOI: |
http://dx.doi.org/10.7148/2011-0289-0295 |
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Abstract: |
Numerical schemes for inverse
problems like volatility estimation or learning market neutral density are of
prime importance for financial planning. Recent advances in numerical techniques
like finite difference solvers based on parallel computation, Monte Carlo for
spectral computations has led to formulation of many approximations based on
these methods for financial instruments. This paper surveys two very
important problems in finance e.g. volatility calibration and timing of order
placing in automatic trading with finite difference discretization
schemes. The methods for volatility calibration are illustrated using
convergence of Euler Pontryagin approximation for a
simplistic model with diffusion price process and then later on more general
price process have also been shown to fit into these frameworks through
similarity of their adjoint equations. The control
approach in algorithmic trading has been done through viscosity solutions and
Lax Friedrich numerical schemes. |
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