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on Market Microstructure |
| By: | Yin Liao; Heather M. Anderson |
| Abstract: | This paper proposes a new test for simultaneous intraday jumps in a panel of high frequency financial data. We utilize intraday first-high-low-last values of asset prices to construct estimates for the cross-variation of returns in a large panel of high frequency financial data, and then employ these estimates to provide a first-high-low-last price based test statistic to detect common large discrete movements (co-jumps). We study the finite sample behavior of our first-high-low-last price based test using Monte Carlo simulation, and find that it is more powerful than the Bollerslev et al (2008) return-based co-jump test. When applied to a panel of high frequency data from the Chinese mainland stock market, our first-high-low-last price based test identifies more common jumps than the return-based test in this emerging market. |
| Keywords: | Covariance, Co-jumps, High-frequency data, First-High-Low-Last price, Microstructure bias, Nonsynchronous trades, Realized covariance, Realized co-range. |
| JEL: | C12 C22 C32 G12 G14 |
| Date: | 2011–08–18 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2011-9&r=mst |
| By: | Felix Naujokat; Ulrich Horst |
| Abstract: | In this article the problem of curve following in an illiquid market is addressed. Using techniques of singular stochastic control, we extend the results of [NW11] to a twosided limit order market with temporary market impact and resilience, where the bid ask spread is now also controlled. We first show existence and uniqueness of an optimal control. In a second step, a suitable version of the stochastic maximum principle is derived which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. The new feature is that we now get a nondegenerate no-trade region, which implies that market orders are only used when the spread is small. This allows to describe precisely when it is optimal to cross the bid ask spread, which is a fundamental problem of algorithmic trading. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders. |
| Keywords: | Stochastic maximum principle, Convex analysis, Fully coupled forward backward stochastic differential equations, Trading in illiquid markets |
| JEL: | C61 G11 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2011-053&r=mst |
| By: | Masato Ubukata (Assistant Professor, Department of Economics, Kushiro Public University of Economics (E-mail: ubukata@kushiro-pu.ac.jp)); Toshiaki Watanabe (Professor, Institute of Economic Research, Hitotsubashi University (E-mail: watanabe@ier.hit-u.ac.jp) Institute for Monetary and Economic Studies, Bank of Japan) |
| Abstract: | This article analyzes whether daily realized volatility, which is the sum of squared intraday returns over a day, is useful for option pricing. Different realized volatilities are calculated with or without taking account of microstructure noise and with or without using overnight and lunch-time returns. ARFIMA, ARFIMAX, HAR, HARX models are employed to specify the dynamics of realized volatility. ARFIMA and HAR models can capture the long-memory property and ARFIMAX and HARX models can also capture the asymmetry in volatility depending on the sign of previous day's return. Option prices are derived under the assumption of risk-neutrality. For comparison, GARCH, EGARCH and FIEGARCH models are estimated using daily returns, where option prices are derived by assuming the risk-neutrality and by using the Duan (1995) method in which the assumption of risk-neutrality is relaxed. Main results using the Nikkei 225 stock index and its put options prices are: (1) ARFIMAX model with daily realized volatility performs best, (2) the Hansen and Lunde ( 2005a) adjustment without using overnight and lunch-time returns can improve the performance, (3) if the Hansen and Lunde (2005a), which also plays a role to remove the bias caused by the microstructure noise by setting the sample mean of realized volatility equal to the sample variance of daily returns, is used, the other methods for taking account of microstructure noise do not necessarily improve the performance and (4) the Duan (1995) method does not improve the performance compared with assuming the risk neutrality. |
| Keywords: | microstructure noise, Nikkei 225 stock index, non-trading hours, option pricing, realized volatility |
| JEL: | C22 C52 G13 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:11-e-18&r=mst |