Informatics and Applications
2024, Volume 18, Issue 1, pp 26-32
MARKET WITH MARKOV JUMP VOLATILITY IV: PRICE OF RISK MONITORING ALGORITHM GIVEN HIGH FREQUENCY OBSERVATION FLOWS OF ASSETS PRICES
Abstract
The fourth part of the series presents a suboptimal algorithm of the market price of risk monitoring given the observations of the underlying and derivative asset prices. As in the previous papers, the market model contains the stochastic volatility described by a hidden Markov jump process. This market has no arbitrage; so, the market price of risk is a function of the Markov process state. The key feature of the investigated market lies in the structure of the available observations. They represent the underlying and derivative prices registered at random instants. The underlying prices are observed accurately, while the derivative prices are corrupted by a random noise. The distribution of the interarrival times between the observable prices and the observation noises depends on the estimated process. The essential feature of the obtained observations is their high arrival intensity compared with the hidden process transition rate. This property allows one to use the central limit theorem for generalized regenerative processes for the filter design. The influence of the estimation performance depending on the observation complexes is illustrated with a numerical example.
[+] References (12)
- Borisov, A. 2023. Rynok s markovskoy skachkoobraznoy volatil'nost'yu I: monitoring tseny riska kak zadacha optimal'noy fil'tratsii [Market with Markov jump volatility I: Price of risk monitoring as an optimal filtering problem]. Informatika i ee Primeneniya - Inform. Appl. 17(2):27-33. doi: 10.14357/19922264230204. EDN: GAXCHQ.
- Borisov, A. 2023. Rynok s markovskoy skachkoobraznoy volatil'nost'yu II: algoritm vychisleniya spravedlivoy tseny derivativov [Market with Markov jump volatility II: Algorithm of derivative fair price calculation]. Informatika i ee primeneniya - Inform. Appl. 17(3):18-24. doi: 10.14357/19922264230303. EDN: DNXJGB.
- Borisov, A. 2023. Rynok s markovskoy skachkoobraznoy volatil'nost'yu III: algoritm monitoringa tseny riska po diskretnym nablyudeniyam tsen aktivov [Market with Markov jump volatility III: Price of risk monitoring algorithm given discrete-time observations of asset prices]. Informatika i ee primeneniya - Inform. Appl. 17(4):9-16. doi: 10.14357/19922264230402. EDN: OFYELT.
- Andersen, T. G., and L. Benzoni. 2009. Stochastic volatility. Complex systems in finance and econometrics. Ed.
R. A. Meyers. New York, NY: Springer. 1:694-726. doi: 10.1007/978-1-4419-7701-4 38.
- Mamon, R. S., and M. R. Rodrigo. 2005. Explicit solutions to European options in a regime-switching economy. Oper. Res. Lett. 33(6):581-586. doi: 10.1016/j.orl. 2004.12.003.
- Boyle, P., and T. Draviam. 2007. Pricing exotic options under regime switching. Insur. Math. Econ. 40(2):267-282. doi: 10.1016/j.insmatheco.2006.05.001.
- Mamon, R. S., and R. Elliott. 2014. Hidden Markov models in finance: Further developments and applications. New York, NY: Springer. Vol. II. 283 p.
- Cvitani‚c, J., R. Liptser, and B. Rozovskii. 2006. A filtering approach to tracking volatility from prices observed at random times. Ann. Appl. Probab. 16(3):1633-1652. doi: 10.1214/105051606000000222.
- Smith, W. 1955. Regenerative stochastic processes. P. Roy. Soc. A - Math. Phy. 232(1188):6-31. doi: 10.1098/ rspa.1955.0198.
- Jacod, J., and A. N. Shiryaev. 2010. Limit theorems for stochastic processes. Berlin: Springer. 664 p.
- Borisov, A., B. Miller, and K. Semenikhin. 2015. Filtering of the Markov jump process given the observations of multivariate point process. Automat. Rem. Contr. 76(2):219- 240. doi: 10.1134/S0005117915020034.
- Scalas, E., R. Gorenflo, H. Luckock, F. Mainardi, M. Mantelli, and M. Raberto. 2004. Anomalous waiting times in high-frequency financial data. Quant. Financ. 4:695-702. doi: 10.1080/14697680500040413.
[+] About this article
Title
MARKET WITH MARKOV JUMP VOLATILITY IV: PRICE OF RISK MONITORING ALGORITHM GIVEN HIGH FREQUENCY OBSERVATION FLOWS OF ASSETS PRICES
Journal
Informatics and Applications
2024, Volume 18, Issue 1, pp 26-32
Cover Date
2024-04-10
DOI
10.14357/19922264240104
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
market price of risk; Markov jump process; high frequency observations; multivariate point process; numerical algorithm
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
|