Volatility Extraction in Information Based Asset Pricing Framework Via Non-Linear Filtering

Cynthia Ikamari, Philip Ngare, Patrick Weke


This study looks at the derivation of a state space model that is applied in non-linear filtering. The model is based on the Brody, Hughson and Macrina information based asset pricing model, also known as the BHM approach or BHM model. The objective of this study is to extend the application of a filtering approach used in estimation of volatilities for the Heston model to the BHM model. The measurement and transition equations obtained in the state space model are used in the extended kalman filter to extract volatility. The option price is obtained from the BS-BHM Updated Model by incorporating information in the Black-Scholes Model. This option price is used to obtain the measurement equation while the variance process is used as the transition equation.


Kalman filter; Extended Kalman Filter; Measurement Equation; Transition Equation; State Space Model.

Full Text:



. A., Macrina (2006). “An Information-Based Framework for Asset Pricing: X-Factor Theory and itsApplications”, PhD Thesis, King’s College London.

. Mutijah, Guritno and Gunardi (2012), “A Black Scholes Model from an Information-Based Perspectiveby Brody Hughston Macrina”, International Conference on Statistics in Science, Business and Engineering.

. Mutijah, Guritno and Gunardi (2013), “Estimation of Parameters on the BS-BHM Updated Model.”Journal Applied Mathematical Sciences.

. D., Brody, L., Hughston and A. Macrina (2008). “Information-based asset pricing”. In: International Journal of Theoretical and Applied finance 11, 107-142.

. Elia Namundjebo (2016). “The Double Heston Model via Filtering Methods”. Msc. Thesis FinancialMathematics in the Faculty of Science at Stellenbosch University.

. Black, Fischer and Scholes, Myron (1973). ”The Pricing of Options and Corporate Liabilities”. In: Journal of Political Economy 81 (3) 637–654.

. Heston Steven (1993). “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”. In The Review of Financial Studies 6(2) 327-343.

. C., Cox,E., Ingersoll and A. Ross (1985). “A Theory of the Term Structure of Interest Rates”. In: Journal of the Econometric Society 53 (2), 385-407.

. H., Albrecher, P., Mayer, W., Schoutens and J., Tistaert (2006). “The little heston trap.”

. Bakshi, Charles and Zhiwu (1997), “Empirical Performance of Alternative Option Pricing Models”. In: The Journal of Finance, 5(2), 46-78.

. C., Ball C and W.Torous (2000). “Stochastic correlation across international stock markets”. In: Journal of Empirical Finance 7, 373-388.

. A. Doucet, N., De Freitas, K., Murphy, and S., Russell (2000). “Rao-blackwellised particle filtering fordynamic bayesian networks”. In: Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence,” 176-183.

. Gatheral, Jim (2006). “The Volatility Surface. A Practitioner’s Guide”. Wiley Finance

. J. Hull. (2008), “Options, Futures and other Derivatives”. Prentice Hall (7), 91-102.

. A., Javaheri. (2005). ”Inside Volatility Arbitrage: the secret of skewness”, Wiley and Sons

. A., Javaheri, D., Lautier and A., Galli. (2003). ”Filtering in finance.” Wilmott, 3.

. S., Julier and J., Uhlmann (1996). “A general method for approximating nonlinear transformations ofprobability distributions.” Tech. Rep., Technical Report, RRG.

. Lewis, Alan (2005), “Option Valuation under Stochastic Volatility: With Mathematica Code” FinancePress (2), Newport Beach, 22-57.

. J., Li (2013). “An unscented kalman smoother for volatility extraction: Evidence from stock prices andoptions.” In: Computational Statistics and Data Analysis, vol. 58, 15-26.

. L., Lu, M., Yang, et al. (2015). “Study on importance function for particle filter.” International Journal of Multimedia and Ubiquitous Engineering, 10(2), 249-258.

. Rouah, F.D. (2013). “The Heston model and its extensions in MATLAB and C#.” John Wiley and Sons.

. R., Van Der Merwe, A., Doucet, N., De Freitas and E., Wan (2000). “The unscented particle filter.” In: NIPS, 2000, 584-590.


  • There are currently no refbacks.





About IJSBAR | Privacy PolicyTerms & Conditions | Contact Us | DisclaimerFAQs 

IJSBAR is published by (GSSRR).