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We analyze the performance of mutual funds from a multiple inference perspective. When the number of funds is large, random fluctuations will cause some funds falsely to appear to outperform the rest. To account for such “false discoveries,” a multiple inference approach is necessary. Discuss this paper
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by Ole E. Barndorff-Nielsen and Neil Shephard In this article we provide a brief review of part of the literature on this topic, focusing on high frequency ex-post measures of volatility and models of volatility driven by L Discuss this paper
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by Amadeo Alentorn The volatility surface implied by option prices presents a structure that changes over time. The aim of this study is to present a framework to model the implied volatility of the FTSE options in real time, and to present a prototype application that implements this framework. We adapt the parametric models presented in Dumas et al (1998) to estimate the surfaces across moneyness instead of across strikes. We discuss how this framework can be used in applications of option pricing and risk management
It has useful information of fundamentals of parameter averaging technique for dynamic SABR model calibration
Abstract: We present the Markovian projection method, a method to obtain closed-form approximations to European option prices on various underlyings that, in principle, is applicable to any (diffusive) model. Successful applications of the method have already appeared in the literature, in particular for interest rate models (short rate and forward Libor models with stochastic volatility), and interest rate/FX hybrid models with FX skew. The purpose of this note is thus not to present other instances where the Markovian projection method is applicable (even though more examples are indeed given) but to distill the essence of the method into a conceptually simple plan of attack, a plan that anyone who wants to obtain European option approximations can follow.
Keywords: Local volatility, stochastic volatility, Markovian projection, parameter averaging, Dupire's local volatility, index options, basket options, spread options
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Original paper by PATRICK S. HAGAN, DEEP KUMAR, ANDREW S. LESNIEWSKI, AND DIANA E. WOODWARD
Abstract. Market smiles and skews are usually managed by using local volatility models a la Dupire. We discover that the dynamics of the market smile predicted by local vol models is opposite of observed market behavior: when the price of the underlying decreases, local vol models predict that the smile shifts to higher prices; when the price increases, these models predict that the smile shifts to lower prices. Due to this contradiction between model and market, delta and vega hedges derived from the model can be unstable and may perform worse than naive Black-Scholes Discuss this paper
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Course Description Lecture 1: The Fundamental Theorem Lecture 2: Multiperiod Models Lecture 3&4: Martingales Lecture 5: Brownian Motion Lecture 6: The Ito Integral Lecture 7: The Black-Scholes Formula Lecture 8: The Cameron-Martin Formula and Barrier Options Lecture 9: Foreign Exchange Lecture 10: Girsanov's Theorem
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by Antoon Pelsser A broad class of exotic interest rate derivatives can be valued simply by adjusting the forward interest rate. This adjustment is known in the market as convexity correction. Various ad hoc rules are used to calculate the convexity correction for different products, many of them mutually inconsistent. In this paper we put convexity correction on a firm mathematical basis by showing that it can be interpreted as the side-effect of a change of probability measure. This provides us with a theoretically consistent framework to calculate convexity corrections. Using this framework we provide exact expressions for libor in arrears, and diff swaps. Furthermore, we propose a simple method to calculate analytical approximations for general instances of convexity correction.
Overview of Monte Carlo Simulation and Probability Review Generating Random Variables and Stochastic Processes The Monte Carlo Framework and Examples from Finance Output Analysis and Run-Length Control Variance Reduction Methods I Variance Reduction Methods II Simulating Stochastic Differential Equations Pricing American Options using Monte Carlo Simulation Discuss this paper
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a small but intersting article by BY TIM BACKSHALL, BARRA INC in www.hedgefundsreview.com quoted - "Innovative efforts to quantify creditworthiness has been a response to changing market conditions in recent years"
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prsenetation by G. Deelstra M. Vanmaele D. Vyncke Risk measures Some well-known risk measures The hedging problem Loss function Risk minimization Multiple risks Convex order, general inverse and comonotonicity Comonotonic sum Non-comonotonic sum Two-additive-factor Gaussian model G2++ Discuss this paper
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prsentation by Jim Gatheral Outline of this talk n A compound Poisson model of stock trading n The relationship between volatility and volume n Clustering n Correlation between volatility changes and log returns n Stochastic volatility n Dynamics of the volatility skew n Similarities between stochastic volatility models n Do stochastic volatility models fit option prices? n Jumps n The impact of large option trades Discuss this paper
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Alos, Elisa and Ewald, Christian-Oliver
We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of the first author [3] in order to derive approximate option pricing formulas in the context of the Heston model. Numerical results are given.
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by Sam Howison Modern financial practice depends heavily on mathematics and a correspondingly large theory has grown up to meet this demand. This paper focuses on the use of matched asymptotic expansions in option pricing; it presents illustrations of the approach in Discuss this paper
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by Hua He Swap spreads, the interest rate differentials between the fixed rates on fixed-for-floating swap contracts and the yields-to-maturity on maturity-matched government bonds, define a market for one of the most actively transacted securities in the global fixed-income arena. A large universe of fixed-income securities including corporate bonds and mortgaged-back securities use interest rate swap spreads as a key benchmark for pricing and hedging. Swap spreads have received renewed attention since the Fall of 1998 when their volatile movements contributed in a significant way to the financial turmoil that led the US Fed to cut short-term interest rates by 75 basis points. In this paper we present new insights on how to analyze term structure of interest swap spreads. Specifically, we focus on the determinants of swap spreads and show how quantities such as the spread of short-term LIBOR over GC-repo rates, the liquidity premium commended by government bonds, and the risk premium required for holding long-term bonds/swaps jointly affect term structures of swap spreads
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Francesca Mariani, Graziella Pacelli, Francesco Zirilli Let us suppose that the dynamics of the stock prices and of their stochastic variance is described by the Heston model, that is by a system of two stochastic differential equations with a suitable initial condition. Our aim is to estimate the parameters of the Heston model and one component of the initial condition, that is the initial stochastic variance, from the knowledge of the stock and option prices observed at discrete times. The option prices considered refer to an European call on the stock whose prices are described by the Heston model. The method proposed to solve this problem is based on a filtering technique to construct a likelihood function and on the maximization of the likelihood function obtained. The estimated parameters and initial value component are characterized as being a maximizer of the likelihood function subject to some constraints. The solution of the filtering problem, used to construct the likelihood function, is based on an integral representation of the fundamental solution of the Fokker-Planck equation associated to the Heston model, on the use of the wavelet expansions presented in [1], [2], [3] to approximate the integral kernel appearing in the representation formula of the fundamental solution, on a simple truncation procedure to exploit the sparsifying properties of the wavelet expansions and on the use of the Fast Fourier Transform (FFT). The use of these techniques generates a very efficient and fully parallelizable numerical procedure to solve the filtering problem, this last fact makes possible to evaluate very efficiently the likelihood function and its gradient. As a byproduct of the solution of the filtering problem we have developed a stochastic variance tracking technique that gives very good results in numerical experiments. The maximum likelihood problem used in the estimation procedure is a low dimensional constrained optimization problem, its solution with ad hoc techniques is justified by the computational cost of evaluating the likelihood function and its gradient. We use parallel computing and a variable metric steepest ascent method to solve the maximum likelihood problem. Some numerical examples of the estimation problem using synthetic data obtained with a parallel implementation of the previous numerical method are presented. Very impressive speed up factors are obtained in the numerical examples using the parallel implementation of the numerical method proposed. This website contains two animations and some auxiliary material that helps the understanding of the paper [7] and makes available to the interested users the computer programs used to produce the numerical experience presented here and in [7] .
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George M. Jabbour* Marat V. Kramin Timur V. Kramin Stephen D. Young This article elaborates an n-order multinomial lattice approach to value derivative instruments on asset prices characterized by a lognormal distribution. Nonlinear optimization is employed, specified moments are matched, and n-order multinomial trees are developed. The proposed methodology represents an alternative specification tomodels of jump processes of order greater than three developed by other researchers. The main contribution of this work is pedagogical. Its strength is in its straightforward explanation of the underlying tree building procedure for which numerical efficiency is a motivation for actual implementation.
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Ren-Raw Chen and Louis Scott This paper presents a method for estimating multi-factor versions of the Cox, Ingersoll, Ross (1985b) model of the term structure of interest rates. The fixed parameters in one, two, and three factor models are estimated by applying an approximate maximum likelihood estimator in a state-space model using data for the U.S. treasury market. A nonlinear Kalman filter is used to estimate the unobservable factors. Multi-factor models are necessary to characterize the changing shape of the yield curve over time, and the statistical tests support the case for two and three factor models. A three factor model would be able to incorporate random variation in short term interest rates, long term rates, and interest rate volatility. Key Words: interest rates, term structure, Kalman filter Discuss this paper
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LCG Rogers This paper introduces a dual way to price American options based on simulating the path of the option payo and of a judiciouslychosen Lagrangian martingale Taking the pathwise maximum of the payo less the martingale provides an upper bound for the price of the option and this bound is sharp for the optimal choice of Lagrangian martingale As a rst exploration of this method four examples are investigated numerically the accuracy achieved with even very simpleminded choices of Lagrangian martingale is surprising The method also leads naturally to candidate hedging policies for the option and estimates of the risk involved in using them
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Matthew C. Pollard Abstract We use the Markov Chain Monte Carlo (MCMC) method to investigate a large class of continuous-time option pricing models. These include: constant-volatility, stochastic volatility, price jump-diffusions and volatility jump-diffusions. Estimation of these models is difficult or impossible by usual statistical methods. Consequently, there is little consensus which model is best. We propose a new Bayesian method for estimation and model selection, the Discuss this paper
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Michael Johannes and Nicholas Polson∗
This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuous-time asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these high-dimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the Clifford-Hammersley theorem, the Gibbs sampler, the Metropolis-Hastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuous-time asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regime-switching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables. Discuss this paper
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Roger Lord Contents �� The Heston model �� The complex logarithm Joint work with Christian Kahl (University of Wuppertal, ABN Discuss this paper
Abstract We use the Malliavin integration by parts formula in order to provide a family of representations of the joint density (which does not involve Dirac measures) of (X,X+), where X is a d-dimensional Markov diffusion (d 1), > 0 and > 0. Following [5], the different representations are determined by a pair of localizing functions. We discuss the problem of variance reduction within the family of separable localizing functions: We characterize a pair of exponential functions as the unique integrated-variance minimizer among this class of separable localizing functions. We test our method on the d-dimensional Brownian motion and provide an application to the problem of American options valuation by the quantization tree method introduced
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Miquel Montero and Arturo Kohatsu-Higa
Abstract In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more exotic derivatives. The Greeks are computed through Monte Carlo simulation.
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ICRA: EC - Early Childhood
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