Share Price Movements in the Post-Credit-Crunch environment TeX Export

@article{citeulike:4919846, abstract = {The market events of 2007-2008 have reinvigorated the search for realistic share price models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market containing both fundamental and technical traders. This is done in a simple way based on a Poisson trade arrival model with variable size orders. With simplifying assumptions we are led to a novel SDE mixing arithmetical and geometric Brownian motions. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive naturally at an equilibrium fat-tailed return distribution with a Pearson Type IV form. Under less restrictive assumptions still richer dynamics are possible. One special case leads to a natural hyperbolic variation of the OU SDE. The phenomenon of variance explosion is identified that gives rise to much larger price movements that might have a priori been expected, so that ``\$25\sigma\$'' events can become more commonplace. We exhibit a solution of the Fokker-Planck equation for a special case that shows how such variance explosion can hide beneath a standard Gaussian facade. This is one member of an extended class of ``inverse-hyperbolic-normal'' distributions with a rich and varied structure, capable of describing a wide range of market behaviours. The Laplace transform of a large sub-class can be given in closed form in terms of Legendre functions, and some further special cases of time-dependent distributions are given. An example of the computation of a hyperbolic VaR is given.}, archivePrefix = {arXiv}, author = {Shaw, William T.}, citeulike-article-id = {4919846}, citeulike-linkout-0 = {http://arxiv.org/abs/0811.0182}, citeulike-linkout-1 = {http://arxiv.org/pdf/0811.0182}, day = {15}, eprint = {0811.0182}, keywords = {environment, in, movements, post-credit-crunch, price, share, the}, month = {Jun}, posted-at = {2009-06-21 09:49:11}, priority = {2}, title = {Share Price Movements in the Post-Credit-Crunch environment}, url = {http://arxiv.org/abs/0811.0182}, year = {2009} }

TY - JOUR ID - citeulike:4919846 L3 - citeulike-article-id:4919846 N2 - The market events of 2007-2008 have reinvigorated the search for realistic share price models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market containing both fundamental and technical traders. This is done in a simple way based on a Poisson trade arrival model with variable size orders. With simplifying assumptions we are led to a novel SDE mixing arithmetical and geometric Brownian motions. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive naturally at an equilibrium fat-tailed return distribution with a Pearson Type IV form. Under less restrictive assumptions still richer dynamics are possible. One special case leads to a natural hyperbolic variation of the OU SDE. The phenomenon of variance explosion is identified that gives rise to much larger price movements that might have a priori been expected, so that ``$25\sigma$'' events can become more commonplace. We exhibit a solution of the Fokker-Planck equation for a special case that shows how such variance explosion can hide beneath a standard Gaussian facade. This is one member of an extended class of ``inverse-hyperbolic-normal'' distributions with a rich and varied structure, capable of describing a wide range of market behaviours. The Laplace transform of a large sub-class can be given in closed form in terms of Legendre functions, and some further special cases of time-dependent distributions are given. An example of the computation of a hyperbolic VaR is given. TI - Share Price Movements in the Post-Credit-Crunch environment KW - environment KW - in KW - movements KW - post-credit-crunch KW - price KW - share KW - the AU - Shaw, William PY - 2009/Jun/15/ UR - http://arxiv.org/abs/0811.0182 ER -