Combining domain knowledge and statistical models in time series analysis

This paper describes a new approach to time series modeling that combines subject-matter knowledge of the system dynamics with statistical techniques in time series analysis and regression. Applications to American option pricing and the Canadian lynx data are given to illustrate this approach.Comment: Published at http://dx.doi.org/10.1214/074921706000001049 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Option pricing using hidden Markov models

Includes bibliographical references (leaves 144-149).This work will present an option pricing model that accommodates parameters that vary over time, whilst still retaining a closed-form expression for option prices: the Hidden Markov Option Pricing Model. This is possible due to the macro-structure of this model and provides the added advantage of ensuring efficient computation of option prices. This model turns out to be a very natural extension to the Black-Scholes model, allowing for time-varying input parameters

Nonlinear Features of Realized FX Volatility

This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives. Dans cet article, nous étudions les caractéristiques nonlinéaires de la dynamique de la volatilité des taux de change à l'aide d'estimations de la volatilité quotidienne basées sur la somme du carré des rendements intraquotidiens. Les erreurs de mesure commises en utilisant la volatilité réalisée pour mesurer la volatilité latente ex post font en sorte que les modèles standards de séries chronologiques de la variance conditionnelle deviennent des variantes d'un modèle ARMAX. Nous explorons des alternatives nonlinéaires à ces spécifications linéaires en utilisant un processus doublement stochastique, avec mixage dépendant de la durée. Ce processus peut capter des changements importants et abrupts dans le niveau de la volatilité, de même qu'une persistence et une variance de la volatilité variant dans le temps. Nos résultats influent sur la précision des prévisions, la couverture et l'évaluation des produits dérivés.High-frequency data, realized volatility, semi-Marko, Données à haute fréquence, volatilité réalisée, demi-Markov

Pricing and Inference with Mixtures of Conditionally Normal Processes.

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.Derivative Pricing ; Stochastic Discount Factor ; Implied Volatility, Mixture of Normal Distributions ; Mixture of Conditionally Normal Processes ; Nonparametric Kernel Estimation ; Mixed-Normal GARCH Processes ; Switching Regime Models.

Linear State Models for Volatility Estimation and Prediction

This report covers the important topic of stochastic volatility modelling with an emphasis on linear state models. The approach taken focuses on comparing models based on their ability to fit the data and their forecasting performance. To this end several parsimonious stochastic volatility models are estimated using realised volatility, a volatility proxy from high frequency stock price data. The results indicate that a hidden state space model performs the best among the realised volatility-based models under consideration. For the state space model different sampling intervals are compared based on in-sample prediction performance. The comparisons are partly based on the multi-period prediction results that are derived in this report

Option pricing with non-Gaussian scaling and infinite-state switching volatility

Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures the above stylized facts, we derive closed form equations for option pricing, obtaining the Black & Scholes as a special case. By applying our pricing equations to a major equity index option dataset, we show that inclusion of stylized features in financial modeling moves derivative prices about 30% closer to the market values without the need of calibrating models parameters on available derivative prices.Comment: Revised version. 31 pages, 4 figure

Martingale representation for contingent claims with regime switching

We derive a martingale representation for a contingent claim under a Markov-modulated version of the Black-Scholes economy. The martingale representation for the price of the claim is established with respect to an equivalent martingale measure chosen by the Esscher transform. Under some differentiability conditions for the coefficients of the price processes, we shall identify explicitly the integrands in the martingale representation using stochastic flows. We shall introduce a zero-coupon bond to minimize the residual risk due to incomplete hedging.14 page(s

Modelling the Dynamics of Credit Spreads of European Corporate Bond Indices

Credit spreads are important financial tools, since they are used as indicators of economic progression, investment decisions, trading and hedging, as well as pricing credit derivatives. Their role has become more significant for the European fixed income markets since the introduction of the Euro, which reshaped the mechanics of the financial environment. The introduction of single currency provided the means for a pan-European economic growth and cross-border development, liberalized a vast inflow of capital which was once fragmented into different currencies, and provided the dynamics of cross-border investments around a unified legislative framework. Thus, the main subject of the thesis is to provide further insight into and investigate the nature and the dynamics of credit spreads of European corporate bond indices during the credit crisis period. Traditional quantitative credit risk models assume that changes in spreads are normally distributed but empirical evidence shows that they are likely to be skewed and fat-tailed, and if they are ignored then the calculation of loss probabilities will be seriously compromised. Therefore, the first area of investigation aims to provide further insight into the dynamics of higher moments and regime shifts in credit spread changes by applying a GARCH-type model that allows for time-varying volatility, skewness and kurtosis, as well as a Markov regime-switching GARCH specification to capture the structural changes in the volatility of credit spreads. Furthermore, a comparison of the different specifications is undertaken in order to assess which model better fits the empirical distribution of the data and produces best Value-at-Risk estimates. The results presented have significant implications for risk management, as well as in the pricing of credit derivatives. The second area of investigation is to assess and evaluate time-varying correlation of credit spreads. Different multivariate GARCH models, such as Orthogonal-GARCH, the Constant and Dynamic Correlation GARCH models, Risk Metrics and Diagonal-BEKK, are applied to examine the behaviour and dynamics of time-varying correlation. Additionally, the performance of the proposed models is examined by determining whether they produce accurate VaR estimates. The study finds evidence in support of time-varying correlation coefficients between credit spreads which appears to be market dependent and has implications for pricing of derivatives, portfolio selection, trading and hedging activities, as well as risk management. Finally, the impact of economic determinants of credit spreads such as the risk-free rate, inflation, as well as equity and commodity indices and volatilities, are investigated over different market conditions using regime switching models. The results highlight how the effect of the determinants on credit spreads varies across different market conditions and point to the existence of non-linear relationship between the determinants and credit spread changes. The study reveals that the regime dependent determinants have significant explanatory power only in the high volatility regime. Finally, it is shown that the feed-forward neural network model out-performs the other specifications applied in this study in terms of estimating out-of-sample mean forecasts

A Regime Switching Model: Estimation, Robustness, and Empirical Evidence

A Regime Switching Model: Estimation, Robustness, and Empirical Evidenc