Top Research Papers on Quantitative Finance

Arbitrage pricing theory underpins the historical growth and contemporary importance of financial derivative markets. The theory is developed systematically for equity, FX, commodity, fixed income, and credit markets. Discrete and continuous time dynamic models of asset prices are studied, developing the analytical insight of standard industry models, numerical schemes, and computational practice. These tools are used routinely by practitioners to value portfolios, hedge risk, determine regulatory capital requirements, and maintain and demonstrate regulatory compliance. The Quantitative Financ...

Quantitative fi nance is a fi eld that has risen to prominence over the last few decades. It encompasses the complex models and calculations that value fi nancial contracts, particularly those which reference events in the future, and apply probabilities to these events. While adding greatly to the fl exibility of the market available to corporations and investors, it has also been blamed for worsening the impact of fi nancial crises. But what exactly does quantitative fi nance encompass, and where did these ideas and models originate? We show that the mathematics behind fi nance and behind games of ...

In this paper, we show how market-technical trends can be calculated automatically from underlying priceprocessesusingastopandreverseprocess.Thebasictoolisasocalledminmaxprocessindicating allrelevantminimaandmaxima.Fortheexistenceoftheminmaxprocess,wegiveaconstructiveproof.Severalsuccessfultrend-followingtradingstrategiescanbeimplementedautomaticallybased onthis1-2-3-trendindicator.

The worlds of Wall Street and The City have always held a certain allure, but in recent years have left an indelible mark on the wider public consciousness and there has been a need to become more financially literate. The quantitative nature of complex financial transactions makes them a fascinating subject area for mathematicians of all types, whether for general interest or because of the enormous monetary rewards on offer. An Introduction to Quantitative Finance concerns financial derivatives - a derivative being a contract between two entities whose value derives from the price of an unde...

1. Introduction 2. Fundamental concepts and techniques 3. Modern portfolio theory 4. Market efficiency 5. Capital structure and dividends 6. Valuing levered projects 7. Option pricing in discrete time 8. Option pricing in continuous time 9. Real options analysis 10. Selected option applications 11. Hedging 12. Agency problems and governance Solutions to exercises Glossary Index.

U radu se pored osnovnih modela financijeske matematike razmatraju i neki prosireni modeli zajmova sa varijabilnim anuitetima. Pored toga razmatraju se i metode ocjene financijskih projekata, posebno s visekriterijalnog aspekta

"What initially looked like an impossible undertaking has become a formidable achievement, stretching from the theoretical foundations to the most recent cutting edge methods. Mille bravos!" - Dr Bruno Dupire (Bloomberg L.P.) The Encyclopedia of Quantitative Finance is a major reference work designed to provide a comprehensive coverage of essential topics related to the quantitative modelling of financial markets, with authoritative contributions from leading academics and professionals. Drawing on contributions from a wide spectrum of experts in fields including financial economics, econometr...

List of Figures . List of Tables. List of Examples . Foreword . Preface to Volume 1 . I.1 Basic Calculus for Finance . I.1.1 Introduction. I.1.2 Functions and Graphs, Equations and Roots. I.1.3 Differentiation and Integration. I.1.4 Analysis of Financial Returns. I.1.5 Functions of Several Variables. I.1.6 Taylor Expansion. I.1.7 Summary and Conclusions. I.2 Essential Linear Algebra for Finance . I.2.1 Introduction. I.2.2 Matrix Algebra and its Mathematical Applications. I.2.3 Eigenvectors and Eigenvalues. I.2.4 Applications to Linear Portfolios. I.2.5 Matrix Decomposition. I.2.6 Principal Com...

1. Interest Rates and Asset Returns. 2. Presentation of Data and Descriptive Statistics. 3. Calculus Applied to Finance. 4. Probability Distributions: Applications to Asset Returns. 5. Statistical Inference: Confidence Intervals and Hypothesis Testing. 6. Regression Analysis. 7. Time Series Analysis. 8. Numerical Methods. 9. Optimization. 10. Continuous Time Mathematics in Finance: Asset Prices as a Stochastic Process. 11. Multivariate Analysis: Principal Components Analysis and Factor Analysis. Appendix: Statistical Tables. Index.

The study analyses stochastic differential equations by showing Ito's lemma and solving the geometric Brown process. Interest rate model is also treated by using the drift condition and affine term structure by analyzing the liquidity and risk premium. Option pricing model is faced by using discretized methods and expected value for vanilla and exotic options with implications for hedging strategies, simulated result is presented with VBA code. Structural model is also considered by using a time dependent default barrier. Portfolio optimization is presented as well with Bayesians applications ...

A financial market model where agents can only trade using realistic buyand-hold strategies is considered. Minimal assumptions are made on the nature of the asset-price process — in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have to be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Mar...

The problem of calculating the optimal dispatch and prices in a single-period electricity auction in a wholesale electricity market is considered here. The novel necessary and sufficient conditions of optimality for this problem are derived and computational algorithms for solving these conditions are constructed.

Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity...

The aim of this paper is to document some empirical facts related to log-returns of diversified world stock indices when these are denominated in different currencies. Motivated by earlier results, we have obtained the estimated distribution of log-returns for a range of world stock indices over long observation periods. We expand previous studies by applying the maximum likelihood ratio test to the large class of generalized hyperbolic distributions, and investigate the log-returns of a variety of diversified world stock indices in different currency denominations. This identifies the Student...

The problem of calculating the optimal dispatch and prices in a single-period electricity auction in a wholesale electricity market is considered here. The novel necessary and sufficient conditions of optimality for this problem are derived and computational algorithms for solving these conditions are constructed.

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer-Schweizer decomposition of a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingaleand variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily const...

We obtain fundamental solutions for PDEs of the form ut = σx uxx + f(x)ux −μxru by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform.

This paper proposes a unified framework for portfolio optimization, derivative pricing, modeling and risk measurement in financial markets with security price processes that exhibit intensity based jumps. It is based on the natural assumption that investors prefer more for less, in the sense that for two given portfolios with the same variance of its increments, the one with the higher expected increment is preferred. If one additionally assumes that the market together with its monetary authority acts to maximize the long term growth of the market portfolio, then this portfolio exhibits a ver...

We extend some known results on a relation between the distribution tails of the continuous local martingale supremum and its quadratic variation to the case of locally square integrable martingale with bounded jumps. The predictable and optional quadratic variations are involved in the main result.

This paper contributes to the development of recent litera ture on the explanation power and calibration issue of heterogeneous asset pricing models by presenting a simple stochastic market fraction asset pricing model of two types of t raders (fundamentalists and trend followers) under a market maker scenario. It seeks to explai n aspects of financial market behaviour (such as market dominance, under and over-reaction, pr fitability and survivability) and to characterize various statistical properties (including a utocorrelation structure) of the stochastic model by using the the dynamics of ...