Market Microstructure and Price Discovery

Affiliation(s)

Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway.

Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway; Department of Functional Analysis, Mechanical and Mathematical Faculty, Belarusian State University, Minsk, Belarus.

Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway.

Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway; Department of Functional Analysis, Mechanical and Mathematical Faculty, Belarusian State University, Minsk, Belarus.

ABSTRACT

The design of this study is to investigate the evolution of a stochastic price process consequent to discrete processes of bids and offers in a market microstructure setting. Under a set of flexible assumptions about agent preferences, we generate a price process to compare with observation. Specifically, we allow for both rational and irrational economic behavior, abstracting the inquiry from classical studies relying on utility theory. The goal is to provide a set of economic primitives which point inexorably to the price processes we see, rather than to assume such process from the start.

Cite this paper

P. Kettler, A. Yablonski and F. Proske, "Market Microstructure and Price Discovery,"*Journal of Mathematical Finance*, Vol. 3 No. 1, 2013, pp. 1-9. doi: 10.4236/jmf.2013.31001.

P. Kettler, A. Yablonski and F. Proske, "Market Microstructure and Price Discovery,"

References

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[2] H. R. Stoll, Elsevier/North-Holland, Amsterdam, 2003.

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[4] E. Eberlein and U. Keller, “Hyperbolic Distributions in Finance,” Bernoulli, Vol. 1, No. 3, 1995, pp. 281-299. doi:10.2307/3318481

[5] T. Bollerslev, “Financial Econometrics: Past Developments and Future Challenges,” Journal of Econometrics, Vol. 100, No. 1, 2001, pp. 41-51. doi:10.1016/S0304-4076(00)00052-X

[6] R. F. Engle, “The Econometrics of Ultra-High-Frequency Data,” Econometrica, Vol. 68, No. 1, 2000, pp. 1-22. doi:10.1111/1468-0262.00091

[7] R. F. Engle and J. R. Russell, “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data,” Econometrica, Vol. 66, No. 5, 1998, pp. 1127-1162. doi:10.2307/2999632

[8] J. Hasbrouck, “The Dynamics of Discrete Bid and Ask Quotes,” The Journal of Finance, Vol. 54, No. 6, 1999, pp. 2109-2142. doi:10.1111/0022-1082.00183

[9] O. Bondarenko, “Competing Market Makers, Liquidity Provision, and Bid-Ask Spreads,” Journal of Financial Markets, Vol. 4, 2001, pp. 269-308. doi:10.1016/S1386-4181(01)00014-3

[10] M. Schaden, “Quantum Finance,” Physica A, Vol. 316, No. 1-4, 2002, pp. 511-538. doi:10.1016/S0378-4371(02)01200-1

[11] S. Hermannn and P. Imkeller, “The Exit Problem for Diffusions with Time Periodic Drift and Stochastic Resonance,” Prepublication No. 01, Institut de Mathématiques élie Cartan, Université Nancy 1, Lorraine, 2003.

[12] P. C. Kettler, O. M. Pamen and F. Proske, “On Local Times: Application to Pricing Using Bid-Ask,” Preprint #13, University of Oslo, Oslo, 2009. www.paulcarlislekettler.net/docs/Oliv.pdf

[13] G. Di Nunno, B. Oksendal and F. Proske, “Malliavin Calculus for Lévy Processes with Applications to Finance,” Universitext, 2nd Edition, Springer, Berlin, 2009.

[14] A. Cartea and T. Meyer-Brandis, “How Does Duration between Trades of Underlying Securities Affect Option Prices?” 2007. http://ssrn.com/abstract=1032714

[1] A. Madhavan, “Market Microstructure: A Survey,” Journal of Financial Markets, Vol. 3, No. 3, 2000, pp. 205258. doi:10.1016/S1386-4181(00)00007-0

[2] H. R. Stoll, Elsevier/North-Holland, Amsterdam, 2003.

[3] O. E. Barndorff-Nielsen, “Processes of Normal Inverse Gaussian Type,” Finance and Stochastics, Vol. 2, No. 1, 1998, pp. 41-68. doi:10.1007/s007800050032

[4] E. Eberlein and U. Keller, “Hyperbolic Distributions in Finance,” Bernoulli, Vol. 1, No. 3, 1995, pp. 281-299. doi:10.2307/3318481

[5] T. Bollerslev, “Financial Econometrics: Past Developments and Future Challenges,” Journal of Econometrics, Vol. 100, No. 1, 2001, pp. 41-51. doi:10.1016/S0304-4076(00)00052-X

[6] R. F. Engle, “The Econometrics of Ultra-High-Frequency Data,” Econometrica, Vol. 68, No. 1, 2000, pp. 1-22. doi:10.1111/1468-0262.00091

[7] R. F. Engle and J. R. Russell, “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data,” Econometrica, Vol. 66, No. 5, 1998, pp. 1127-1162. doi:10.2307/2999632

[8] J. Hasbrouck, “The Dynamics of Discrete Bid and Ask Quotes,” The Journal of Finance, Vol. 54, No. 6, 1999, pp. 2109-2142. doi:10.1111/0022-1082.00183

[9] O. Bondarenko, “Competing Market Makers, Liquidity Provision, and Bid-Ask Spreads,” Journal of Financial Markets, Vol. 4, 2001, pp. 269-308. doi:10.1016/S1386-4181(01)00014-3

[10] M. Schaden, “Quantum Finance,” Physica A, Vol. 316, No. 1-4, 2002, pp. 511-538. doi:10.1016/S0378-4371(02)01200-1

[11] S. Hermannn and P. Imkeller, “The Exit Problem for Diffusions with Time Periodic Drift and Stochastic Resonance,” Prepublication No. 01, Institut de Mathématiques élie Cartan, Université Nancy 1, Lorraine, 2003.

[12] P. C. Kettler, O. M. Pamen and F. Proske, “On Local Times: Application to Pricing Using Bid-Ask,” Preprint #13, University of Oslo, Oslo, 2009. www.paulcarlislekettler.net/docs/Oliv.pdf

[13] G. Di Nunno, B. Oksendal and F. Proske, “Malliavin Calculus for Lévy Processes with Applications to Finance,” Universitext, 2nd Edition, Springer, Berlin, 2009.

[14] A. Cartea and T. Meyer-Brandis, “How Does Duration between Trades of Underlying Securities Affect Option Prices?” 2007. http://ssrn.com/abstract=1032714