A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback
| Autor: | William T. Shaw, Marcus Schofield |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Quantitative Finance. 15:975-998 |
| ISSN: | 1469-7696 1469-7688 |
| DOI: | 10.1080/14697688.2011.642810 |
| Popis: | Recent market events have reinvigorated the search for realistic return models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market with both fundamental and technical traders. This is based on a trade arrival model with variable size orders and a general arrival-time distribution. With simplifications we are led in the jump-free case to a local volatility model defined by a hybrid SDE mixing both arithmetic and geometric or CIR Brownian motions, whose solution in the geometric case is given by a class of integrals of exponentials of one Brownian motion against another, in forms considered by Yor and collaborators. The reduction of the hybrid SDE to a single Brownian motion leads to an SDE of the form considered by Nagahara, which is a type of ‘Pearson diffusion’, or, equivalently, a hyperbolic OU SDE. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive natural... |
| Databáze: | OpenAIRE |
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