Informatics and Applications
2023, Volume 17, Issue 2, pp 27-33
MARKET WITH MARKOV JUMP VOLATILITY I: PRICE OF RISK MONITORING AS AN OPTIMAL FILTERING PROBLEM
Abstract
The first part of series is devoted to investigating the market price of risk in a financial system. It contains riskless bank deposits, risky base assets, and their derivatives. The model ofthe underlying price evolution represents a stochastic differential system with stochastic volatility which is a hidden Markov jump process. The investigated market is incomplete and has no arbitrage possibilities. The market price ofrisk, which corresponds to a prevailing martingale measure, can be characterized via the hidden Markov jump process but can not be restored precisely. However, it can be estimated optimally using the observations of both the derivative and underlying prices. Using the concept of the prevailing martingale measure existence, one can derive a system of the partial differential equations which describes an evolution of the derivative prices and represents some analog of the classic Black-Sholes equation. Then, one can convert the calculation problem for the market price of risk to the optimal state filtering in a differential stochastic observation system. The paper also discusses various aspects ofthe numerical realization for the stated estimation problem.
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[+] About this article
Title
MARKET WITH MARKOV JUMP VOLATILITY I: PRICE OF RISK MONITORING AS AN OPTIMAL FILTERING PROBLEM
Journal
Informatics and Applications
2023, Volume 17, Issue 2, pp 27-33
Cover Date
2023-07-10
DOI
10.14357/19922264230204
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; optimal filtering; diffusion and counting observations; multiplicative observation noise; numerical approximation accuracy
Authors
A. V. Borisov 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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