Daily Archives July 12, 2015

The Daniels Model (2003)

The first example of this model was presented in Daniels et al. (2003). After that there were a few papers published with an analysis of this model (Farmer et al. 2005, 2006). The main assumption of this model was that orders are come onto the market randomly. There are market orders that are executed immediately and limit orders, which are placed at a fixed price level and executed only when there is a counter-party on the market which wants to trade at this price. All orders have an intensity of incoming, an intensity of canceling, a volume and a price (see Fig. 1). All these parameters can be measured using empirical data, and this is the main advantage of this model. We try to create a model as in the original papers.

For the estimation of parameter a we calculated the difference betwe...

Comparison of Portfolio Management Strategies

Despite the great potential of the developed models, most of them have not been applied to real data. To prove the usefulness of portfolio management models for practitioners, we apply some of the contemporary results in this field to real MICEX trading data and give recommendations for their usage. Our database consists of the complete tick-by-tick limit order book for MICEX shares from January 2006 through June 2007. We consider only liquid shares, such as LKOH, RTKM and GAZP, because only during sufficiently intensive trading does it become possible to calibrate models for the real market.

We consider the problem of optimal purchase of a single-asset portfolio over a given period and compare the performance of the following strategies:

1...

Overview of Contemporary Portfolio Management Models and Their Evolution

Davis and Norman (1990) introduced a consumption-investment problem for a CRRA agent with proportional transaction costs and obtained a closed-form solution for it. Another advantage of the model was allowing for discontinuous strategy. For this purpose, the original Merton framework had to be upgraded to semimartingale dynamics. Portfolio value in each of the assets is described by the following equations:

dXt = (rtXt — Ct) dt — (1 + A) dLt + (1 — p) dMt, X0 = x,

dY t = aYt dt + oYt dwt + dLt — dMt, Y0 = y,

where coefficients A, p define proportional transaction costs, Lt, Mt are cumulative amounts of bought and sold risky asset respectively. Results demonstrated the existence of three behavioral regions for portfolio managers, and are presented in Fig. 3.

Unlike Merton’s case, th...

Publishing Switzerland 2015

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Contemporary Price Impact Modeling

The ideal frictionless market of Merton (1969) does not adequately simulate the more complex real market. First of all, price dynamics obviously depend on an agent’s actions in the market; moreover, there is no single characteristic of an asset’s market value (price). Since the 1990s, electronic trading through limit order books (LOB) has been gaining popularity, providing the market with a set of orders with different volumes and prices during any trading period. Inability to close a deal at an estimated price led to the necessity of including transaction costs in portfolio management models and price impact modeling. For the past two decades, research in this field has provided complex models that allow for time varying forms of LOBs, temporary and permanent price impact, resilience etc...

Mathematical Models of Price Impact and Optimal Portfolio Management in Illiquid Markets

Nikolay Andreev

Abstract The problem of optimal portfolio liquidation under transaction costs has been widely researched recently, producing several approaches to problem formulation and solving. Obtained results can be used for decision making during portfolio selection or automatic trading on high-frequency electronic markets. This work gives a review of modern studies in this field, comparing models and tracking their evolution. The paper also presents results of applying the most recent findings in this field to real MICEX shares with high-frequency data and gives an interpretation of the results.

Keywords Market liquidity • Optimal portfolio selection • Portfolio liquidation • Price impact

JEL Classification C61, G11

1 Introduction

With the development of electronic trading plat...