We propose a market-consistent approach to the definition and construction of the implied term structure of the risk-free interest rates which are model-independent with respect to the choice of the fitting method. The main idea consists of the simultaneous fitting of the credit default swap (CDS) and the defaultable bond quotes where the theoretical prices are calculated in the framework of the reduced-form modelling of credit risk under standard assumptions. We obtain not only the implied risk-free zero-coupon yield curve but also the implied issuer-specific hazard rate curves. Prior to fitting, we perform a selection of bond issues and issuers. Next, we check for data consistency via arbitrage-like reasoning. Typically, the initial data needs a consistency adjustment, namely `artificial' widening of the observed bid-ask spreads for the selected financial instruments. We construct feasibility bands representing achievable precision of the fitting procedure depending on maturity. Then we apply this methodology to determine the term structure of the risk-free rates for the euro zone. This generic approach for the calculation of the risk-free reference rates in the euro zone can be helpful for the purposes of insurers and pension funds. In particular, the relevant term structure can be used in the assessment of technical provisions as requested in Article 77 of the Solvency II Level 1 text.
We use the linear programming approach to quantify quote inconsistencies in risk-free bond markets. We present an algorithm to identify whether an inconsistency is probably due to the insufficient framework flexibility, the insufficient data quality, or the non-homogeneity of the dataset. In the latter case we study the problem of filtering out some instruments so that the remaining dataset be homogeneous. We show that the traditional filtering approach performs unacceptably poor and propose new algorithms. We find that the bonds, which get mispriced the most by a fitting algorithm, surprisingly are not the bonds, which cause the inconsistencies.
We present a nonparametric method for fitting the term structure of interest rates from bond prices. Our method is a variant of the smoothing spline approach, but within our framework we are able to determine the smoothing coefficient automatically from data using the generalized cross-validation or maximum likelihood estimates. We present an effective numerical algorithm to simultaneously find the term structure and the optimal smoothing coefficient. Finally, we compare the proposed nonparametric fitting method with other parametric and nonparametric methods to find its superior performance. We find that existing term structure fitting methods perform well in liquid markets while illiquid markets present new challenges, which we address in this article.
Research of nonlinear dynamics of finance series has been widely discussed in literature since the 1980s with chaos theory as the theoretical background. Chaos methods have been applied to the S&P 500 stock index, stock returns from the UK and American markets, and portfolio returns. This work reviews modern methods as indicators of nonlinear stochastic behavior and also shows some empirical results for MICEX stock market high-frequency microstructure variables such as stock price and return, price change, spread and relative spread. It also implements recently developed recurrence quantification analysis approaches to visualize patterns and dependency in microstructure data.
The problem of optimal portfolio liquidation under transaction costs has been widely researched recently, thus producing several approaches to problem formulation and solving. Obtained results can be used for decision making during portfolio selection or automatic trading at 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 high-frequency data and gives an interpretation of the results.
Econophysics is a relatively new discipline. It is one of the most interesting and promising trends in modeling complex economic systems such as financial markets. In this paper we use the approach of econophysics to explain various mechanisms of price formation in the stock market. We study a model, which was proposed by Jean-Philippe Bouchaud and Dietrich Stauffer (Bouchaud 2002; Chang et al. 2002; Stauffer 2001; Stauffer and Sornette 1990), and used to describe the agents’ cooperation in the market. The most important point of this research is the calibration of the model, using real market conditions to proof the model’s possibility of setting out a real market pricing process
The aim of this paper is to consider some problems with evaluation of the impact of high frequency trading on market liquidity. The first part is devoted to difficulties of disentangling the impact of high frequency on market liquidity from other relevant factors. The remainder of the paper is intended to discuss some issues affecting the evaluation of the influence of high frequency trading on particular aspects of market liquidity.