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on Market Microstructure |
| By: | Fulvio Baldovin; Francesco Camana; Massimiliano Caporin; Attilio L. Stella |
| Abstract: | We demonstrate that a stochastic model consistent with the scaling properties of financial assets is able to replicate the empirical statistical properties of the S&P 500 high frequency data within a window of three hours in each trading day. This result extends previous findings obtained for EUR/USD exchange rates. We apply the forecast capabilities of the model to implement an explicit trading strategy. Trading signals are model-based and not derived from chartist criteria. In-sample and out-of-sample tests indicate that the model performs better than a benchmark asymmetric GARCH process, and expose the existence of small arbitrage opportunities. We discuss how to improve performances and why the trading strategy is potentially interesting to hedge volatility risk for S&P index-based products. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.2447&r=mst |
| By: | Scalas, Enrico; Politi, Mauro |
| Abstract: | A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools. -- |
| Keywords: | Option pricing,high-frequency finance,high-frequency trading,computer trading,jump-diffusion models,pure-jump models,continuous time random walks,semi-Markov processes |
| JEL: | G13 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:201214&r=mst |
| By: | Luciano Campi; Umut \c{C}etin; Albina Danilova |
| Abstract: | Given a Markovian Brownian martingale $Z$, we build a process $X$ which is a martingale in its own filtration and satisfies $X_1 = Z_1$. We call $X$ a dynamic bridge, because its terminal value $Z_1$ is not known in advance. We compute explicitly its semimartingale decomposition under both its own filtration $\cF^X$ and the filtration $\cF^{X,Z}$ jointly generated by $X$ and $Z$. Our construction is heavily based on parabolic PDE's and filtering techniques. As an application, we explicitly solve an equilibrium model with insider trading, that can be viewed as a non-Gaussian generalization of Back and Pedersen's \cite{BP}, where insider's additional information evolves over time. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.2980&r=mst |