Abstract
By utilizing information about prices and trading volumes, we discuss the pricing of European contingent claims in a continuous-time hidden regime-switching environment. Hidden market sentiments described by the states of a continuous-time, finite-state, hidden Markov chain represent a common factor for an asset’s drift and volatility, as well as its trading volumes. Using observations about trading volumes, we present a filtered estimate of the hidden common factor. The asset pricing problem is then considered in a filtered market, where the hidden drift and volatility are replaced by their filtered estimates. We adopt the Esscher transform to select an equivalent martingale measure for pricing and derive a partial-differential integral equation for the option price.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersen, T. G. (1996). Return volatility and trading volume: An information flow interpretation of stochastic volatility. Journal of Finance, 51, 169–204.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.
Buffington, J., & Elliott, R. J. (2001). American options with regime switching. International Journal of Theoretical and Applied Finance, 5, 497– 514.
Bühlmann, H., Delbaen, F., Embrechts, P., & Shiryaev, A. N. (1996). No-arbitrage, change of measure and conditional esscher transform. CWI Quarterly, 9(4), 291–317.
Bühlmann, H., Delbaen, F., Embrechts, P., & Shiryaev, A. (1998). On Esscher transforms in discrete finance models. ASTIN Bulletin, 28, 171–186.
Clark, P. K. (1973). A subordinated stochastic process with finite variance for speculative prices. Econometrica, 41, 135–156.
Clark, J. M. C. (1978). The design of robust approximations to the stochastic differential equations for nonlinear filtering. In J. K. Skwirzynski (Ed.), Communications systems and random process theory (pp. 721–734). The Netherlands: Sijthoff and Noorhoff.
Elliott, R. J., Aggoun, L., & Moore, J. B. (1994). Hidden Markov models: Estimation and control. Berlin: Springer.
Elliott, R. J., & Malcolm, W. P. (2005). General smoothing formulas for Markov-modulated poisson observations. IEEE Transactions on Automatic Control, 50(8), 1123–1134.
Elliott, R. J., Chan, L., & Siu, T. K. (2005). Option pricing and Esscher transform under regime switching. Annals of Finance, 1(4), 423–432.
Elliott, R. J., & Siu, T. K. (2013) Option pricing and filtering with hidden markov-modulated pure jump processes. Applied Mathematical Finance, 20(1), 1–25.
Epps, T. W. (1975). Security price changes and transaction volumes: Theory and evidence. American Economic Review, 65, 586–597.
Epps, T. W., & Epps, M. L. (1976). The stochastic dependence of security price changes and transaction volumes: Implications for the mixture-of-distributions hypothesis. Econometrica, 44, 305–321.
Gallant, A. R., Rossi, P. E., & Tauchen, G. (1992). Stock prices and volume. Review of Financial Studies, 5, 199–242.
Gerber, H. U., & Shiu, E. S. W. (1994). Option pricing by Esscher transforms (with discussions). Transactions of the Society of Actuaries, 46(6), 99–191.
Lo, A., & Wang, J. (2006). Trading volume: Implications of an intertemporal capital asset pricing model. Journal of Finance, 61, 2805–2840.
Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381–408.
Harrison, J. M., & Pliska, S. R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications, 11, 215–280.
Harrison, J. M., & Pliska, S. R. (1993). A stochastic calculus model of continuous trading: Complete markets. Stochastic Processes and Their Applications, 15, 313–316.
Guo, X. (2001) Information and option pricings. Quantitative Finance 1, 38–44.
Merton, R. C. (1973). The theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183.
Ono, S. (2006). Option pricing under stochastic volatility and trading volume. Preprint. University of York.
Shalen, C. T. (1993). Volume, volatility, and the dispersion of beliefs. Review of Financial Studies, 6, 405–434.
Siu, T. K. (2008). A game theoretic approach to option valuation under Markovian regime-switching models. Insurance: Mathematics and Economics, 42(3), 1146–1158.
Siu, T. K. (2011). Regime switching risk: To price or not to price? International Journal of Stochastic Analysis, Article ID 843246
Siu, T.K. (2014a). A hidden markov-modulated jump diffusion model for european option pricing. In R. Mamon & R. J. Elliott (Eds.), Hidden markov models in finance (Vol. 2, pp. 185–209). New York:Springer.
Siu, T.K. (2014b). American option pricing and filtering with a hidden regime-switching jump diffusion. Preprint.
Tauchen, G., & Pitts, M. (1983). The price variability-volume relationship on speculative markets. Econometrica, 51, 485–505.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Elliott, R.J., Siu, T.K. Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment. Asia-Pac Financ Markets 22, 133–149 (2015). https://doi.org/10.1007/s10690-014-9197-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10690-014-9197-4