9th Joint International Conference on Information Sciences (JCIS-06)

Learning Martingale Measures From High Frequency Financial Data to Help Option Pricing

Authors
Hung-Ching (Justin) Chen 0, Malik Magdon-Ismail
Corresponding Author
Hung-Ching (Justin) Chen
0Rensselaer Polytechnic Institute
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DOI
https://doi.org/10.2991/jcis.2006.126How to use a DOI?
Keywords
Financial Derivative, Martingale, Risk Neutral, Pricing
Abstract
We provide a framework for learning risk-neutral measures (Martingale measures) for pricing options from high frequency financial data. In a simple geometric Brownian motion model, a price volatility, a fixed interest rate and a no-arbitrage condition suffice to determine a unique risk-neutral measure. On the other hand, in our framework, we relax some of these assumptions to obtain a class of allowable risk-neutral measures. We then propose a framework for learning the appropriate risk-neural measure. Since the risk-neutral measure prices all options simultaneously, we can use all the option contracts on a particular underlying stock for learning. We demonstrate the performance of these models on historical data. In particular, we show that both learning without a no-arbitrage condition and a no-arbitrage condition without learning are worse than our framework; however the combination of learning with a no-arbitrage condition has the best result. These results indicate the potential to learn Martingale measures with a no-arbitrage condition providing just the right constraint. We also compare our approach to standard Binomial models with volatility estimates (historical volatility and GARCH volatility predictors). Finally, we illustrate the power of such a framework by developing a real time trading system based upon these pricing methods.
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Proceedings
9th Joint International Conference on Information Sciences (JCIS-06)
Publication Date
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ISBN
978-90-78677-01-7
DOI
https://doi.org/10.2991/jcis.2006.126How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Hung-Ching (Justin) Chen
AU  - Malik Magdon-Ismail
PY  - NaN/NaN
DA  - NaN/NaN
TI  - Learning Martingale Measures From High Frequency Financial Data to Help Option Pricing
BT  - 9th Joint International Conference on Information Sciences (JCIS-06)
PB  - Atlantis Press
UR  - https://doi.org/10.2991/jcis.2006.126
DO  - https://doi.org/10.2991/jcis.2006.126
ID  - ChenNaN/NaN
ER  -