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This paper presents a new framework for credit value adjustment (CVA) that is a relatively new area of financial derivative modeling and trading. In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of accuracy with a relatively easy implementation. We find that the prices of risky contracts are normally determined via backward induction when their payoffs could be positive or negative. Moreover, the model can naturally capture wrong or right way risk.
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The LIBOR Market Model (LMM or BGM) has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice/tree (BGM tree or BGM lattice) approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.
Key Words: LIBOR Market Model (LMM or BGM), lattice model, tree model, shifted forward measure, drift approximation, risk management, calibration, callable exotics, callable bond, callable capped floater swap, callable inverse floater swap, callable range accrual swap. Discuss this paper
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A book on lot of topics in QF by Wolfgang hardle, Torsten Kleinow, Gerhard Stahl Examples are based on a proprietery software called quantlet, can be downloaded from http://fedc.wiwi.hu-berlin.de/xplore.php
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by Maria Pacurar Abstract. This paper provides an up-to-date survey of the main theoretical developments in ACD modeling and empirical studies using financial data. First, we discuss the properties of the standard ACD specification and its extensions, existing diagnostic tests, and joint models for the arrival times of events and some market characteristics. Then, we present the empirical applications of ACD models to different types of events, and identify possible directions for future research. Keywords: Autoregressive Conditional Duration model, tick-by-tick data, duration clustering, marked point process, market microstructure, asymmetric information, Value at Risk.
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by Guillaume Weisang Abstract: This paper has two goals. First, this paper reviews the family of Augmented Autoregressive Conditional Duration (AACD) models. Second, I provide source code for the estimation of some linear ACD models as well as examples of empirical applications. A warning is needed however: this is part of an ongoing work. Please report to the author any mistake. Your comments will be most appreciated as well.
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We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main processes. By an appropriate change of measure the dimension of the corresponding pricing PDE can be greatly reduced. We place by a number of approximations the model in the class of affine processes [DPS00], for which we then provide the corresponding forward characteristic function. We discuss in detail the accuracy of the approximations and the efficient calibration. Finally, by experiments, we show the effect of the correlations and interest rate smile/skew on typical equity-interest rate hybrid product prices. For a whole strip of strikes this approximate hybrid model can be evaluated for equity plain vanilla options in just milliseconds. Discuss this paper
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by Eric Zivot A key problem in financial econometrics is the modeling, estimation and forecasting of conditional return volatility and correlation. Having accurate forecasting models for conditional volatility and correlation is important for accurate derivatives pricing, risk management and asset allocation decisions. It is well known that conditional volatility and correlation are highly predictable. An inherent problem with modeling and forecasting conditional volatility is that it is unobservable, which implies that modeling must be indirect. Popular parametric models for latent volatility include the ARCH-GARCH family, the stochastic volatility family, and the Markov-switching family. In these models volatility is usually extracted from daily squared returns, which are unbiased but noisy estimates of daily conditional volatility. High frequency data is rarely utilized. The estimation of these models, however, often give unsatisfactory results. In particular, forecasts are imprecise. Moreover, standardized returns generally have fat-tails which has led to the search for appropriate error distributions that can adequately capture empirical return distributions. Furthermore, multivariate modeling of volatility and correlation can be extremely difficult and practical models are often only feasible for very low dimensions.
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by Eric Zivot High-frequency financial data are observations on financial variables taken daily or at a finer time scale, and are often irregularly spaced over time. Advances in computer technology and data recording and storage have made these data sets increasingly accessible to researchers and have driven the data frequency to the ultimate limit for some financial markets: time stamped transaction-by-transaction or tick-by-tick data, referred to as ultra-high-frequency data by Engle (2000). For equity markets, the Trades and Quotes (TAQ) database of the New York Stock Exchange (NYSE) contains all recorded trades and quotes on NYSE, AMEX, NASDAQ, and the regional exchanges from 1992 to present. The Berkeley Options Data Base recorded similar data for options markets from 1976 to 1996. In foreign exchange markets, Olsen Associates in Switzerland maintains a data base of indicative FX spot quotes for many major currency pairs published over the Reuters Discuss this paper
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by Bingcheng Yan and Eric Zivot High-frequency financial data are observations on financial variables taken daily or at a finer time scale, and are often irregularly spaced over time. Advances in computer technology and data recording and storage have made these data sets increasingly accessible to researchers and have driven the data frequency to the ultimate limit for some financial markets: time stamped transaction-by-transaction or tick-by-tick data, referred to as ultra-high-frequency data by Engle (2000). For equity markets, the Trades and Quotes (TAQ) database of the New York Stock Exchange (NYSE) contains all recorded trades and quotes on NYSE, AMEX, NASDAQ, and the regional exchanges from 1992 to present. The Berkeley Options Data Base recorded similar data for options markets from 1976 to 1996. In foreign exchange markets, Olsen Associates in Switzerland maintains a data base of indicative FX spot quotes for many major currency pairs published over the Reuters Discuss this paper
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Jonathon Shlens Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but poorly understood. The goal of this paper is to dispel the magic behind this black box. This tutorial focuses on building a solid intuition for how and why principal component analysis works; furthermore, it crystallizes this knowledge by deriving from simple intuitions, the mathematics behind PCA . This tutorial does not shy away from explaining the ideas informally, nor does it shy away from the mathematics. The hope is that by addressing both aspects, readers of all levels will be able to gain a better understanding of PCA as well as the when, the how and the why of applying this technique. Discuss this paper
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by Martin le Roux In this paper we present an econometric model of implied volatilities of S&P500 index options. Firstly, we model the dynamics the CBOE VIX index as a proxy for the general level of implied volatilities. We then describe a parametric model of the implied volatility surface for options with a term of up to two years. We show that almost all of the differences between the VIX and the implied volatility surface (i.e. smile and term structure effects) can be explained by one or two uncorrelated random factors. Finally, we present a model of the dynamics of these factors
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by Dr. Reinhold Hafner, Dr. Bernd Schmid Abstract We present a factor-based model of the stochastic evolution of the implied volatility surface. The model allows for the integrated and consistent pricing and hedging, risk management, and trading of equity index derivatives as well as volatility derivatives. We develop a unifying theory for the analysis of contingent claims under both the realworld measure and the risk-neutral measure in an environment of stochastic implied volatility. On the basis of transaction data, we provide extensive statistical analyses on the dynamics of the implied volatility surface of German DAX options and propose a four-factor model to describe its evolution. The model is validated and tested on market data.
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by A.R. Radhakrishnan Convergence rate and accuracy of the non-recombining HJM forward rate tree are tested by constructing a tree for the forward rate process equivalent to the Hull-White short rate process. Put option values on a ten-year discount bond from the forward rate tree are compared to the accurate values obtained from a recombining short rate lattice. European option values from the HJM tree converge to the true value in twelve steps for all option maturities up to twenty-five years. American option values are within a cent or two of the accurate values for one and five-year options, but do not converge to the accurate value in twenty-four steps, the maximum attempted, for higher maturities. At-the-money options are underpriced by one percent for ten-year maturity and by more than three percent for twenty-five year maturity. Out-of-the-money options are underpriced by up to nine percent. Results are independent of the shape of the initial term structure. Using an HJM tree with equal stepsizes leads to more accurate values for European options, but a tree with linearly increasing stepsizes performs better in the case of American options. It is found optimal to have the same number of forward rates maturing per year beyond option maturity as the number of steps per year through option maturity. Discuss this paper
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Eric Benhamou (London School of Economics) Alexandre Duguet (London School of Economics) This paper presents a new method for the pricing of discrete Asian options when assuming a deterministic volatility as specified in Dupire (1993). Using a homogeneity property, we show how to reduce an n+1 dimensional problem to a 2 dimensional one. Previous research has been intensively focussing on continuous time Asian options using Black Scholes assumptions. However, traded Asian options are based on a discrete time sampling and can exhibit a pronounced volatility smile. Previous works which have tried to find approached closed forms have the major drawback to be not extendable to more complex volatility model, like the Dupire model, as well as to American type options: Vorst (1992), Geman and Yor (1993), Turnbull and Wakeman (1991), Levy (1992), Jacques (1995), Zhang (1997) and Milevsky and Posner (1998). Works which have focussed at numerical methods do not take into account volatility smile and focus at continuous Asian options: Kemma and Vorst (1990), Hull and White (1993), Caverhill and Clewlow (1990), Benhamou (1999), Roger and Shi (1995), He and Takahashi (1996), Alziary et al. (1997) and Zvan et al. (1998). Our paper o Discuss this paper
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thesis by Andreas J. Grau This work will focus on pricing and hedging of derivatives with Monte Carlo simulation. In some cases, direct numerical PDE solutions will be used as a reference. We will provide insight into the versatile applications of regression methods for the Monte Carlo valuation. As a result, very fast valuation procedures are developed: In some cases the methods developed in this dissertation are the first of its kind which handle specific exotic options. Especially the pricing of a high-dimensional MovingWindow Asian option with early exercise and the implementation of a moving window soft-call constraint of convertible bonds are solved for the first time in this thesis. Prior technology could not cope with the high-dimensional pricing problem together with an early exercise feature. The PDE method can deal with an early exercise feature easily, but high-dimensional problems are unfeasible. Monte Carlo methods can deal with high-dimensional problems, but an early exercise of a high-dimensional option pricing problem is hard to treat correctly in the previous setting. Another contribution of this thesis is the Simulation-Based Hedging method which connects realistic models for the underlying with suitable pricing and hedging without a detour to a socalled risk-neutral measure. The Simulation-Based Hedging has extraordinary properties: E.g. using the Black-Scholes assumptions its convergence to the Black-Scholes prices is much faster than the comparable Longstaff-Schwartz Least-Squares Monte Carlo [81]. Furthermore, the underlying can follow any real-world process: The algorithm always computes the optimal hedging strategy and thus attains realistic risk-adjusted prices and hedges. This can also be done using multiple hedge instruments. Consequently, the new Simulation-Based Hedging is a new pricing framework together with a numerical method for the solution to option pricing problems in so called incomplete markets. The whole setting of the framework is new, but related to risk minimization techniques for optimal hedging of financial options presented by several authors [46, 95, 47, 33]). Especially, the setting of Simulation-Based Hedging can be seen as an extension to the variance minimization presented by Schweizer [104] and the presented numerical solution is related to a method presented by Potters et. al. [96] resp. Pochart and Bouchaud
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by Tian-Shyr Dai,Guan-Shieng Huang,Yuh-Dauh Lyuu Financial options whose payoff depends critically on historical prices are called pathdependent options. Their prices are usually harder to calculate than options whose prices do not depend on past histories. Asian options are popular path-dependent derivatives, and it has been a long-standing problem to price them efficiently and accurately. No known exact pricing formulas are available to price them under the continuous-time Black Discuss this paper
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could not get info on title and author I found this while surfing, looks interesting. Discusses several topics in Quant finance Discuss this paper
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Thesis by Christa Cuchiero The aim of this diploma thesis is to present the theory as well as the practical applications of affine interest rate models. On the basis of the general theory established by Duffie and Kan, we put emphasis on affine models whose state variables have - in contrast to their theoretical abstract definition - a reasonable economic interpretation. Starting from the very first term structure models, namely the Vasicek and the Cox-Ingersoll-Ross model, we describe in sequel two- and more-factor models that have appeared in literature. By means of the Vasicek model we exemplify the calibration to market yields as well as to market cap volatilities. However, our main focus are affine yield factor models developed by Duffie and Kan, which allow to relate the state variables to yields with different maturities. We show how to calibrate a two-factor version of this model to market data. The results are promising since the model fits the market yields from different dates very well while the parameters remain nearly constant Discuss this paper
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by Lawrence C. Evans Chapter 1: Introduction Chapter 2: A crash course in basic probability theory Chapter 3: Brownian motion and Discuss this paper
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by Beata Stehlıkov In short rate interest rate models, the behaviour of the short rate is given by a stochastic differential equation (1-factor models) or a system of stochastic differential equations (multifactor models). Interest rates with different maturities are determined by bond prices, which are solutions of the parabolic partial differential equation. We consider the generalized 2-factor Vasicek model and Fong-Vasicek model with stochastic volatility. In the 2-factor Vasicek model, the short rate is a sum of two independent Ornstein-Uhlenbeck processes. The bond price is a function of maturity and level of each of the components of the short rate. In Fong-Vasicek model, the volatility of the short rate is stochastic. The bond price is a function of maturity, short rate and volatility. In both cases, we do not observe all values necessary to obtain a bond price. Therefore, we propose the averaging of the bond prices. We consider the limiting probability distribution of unobservable variables. In this way, we obtain the averaged bond prices depending only on the maturity and short rate. We prove that there is no 1-factor model yielding the same bond prices as are the averaged values described above.
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slides of lecture notes: Table of contents I. Introduction to Stochastic Processes II. Basic Concepts II.1 Mathematical Techniques of Time Series Analysis II.2 (Stochastic) Di Discuss this paper
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by Peter Schotman In this paper we propose and implement a Bayesian procedure for the empirical valuation of bond options given the observed term structure of interest rates, and given assumptions about the time series behavior of the instantaneous spot rate. The Bayesian approach is motivated by the extreme multicollinearity in the cross-sectional data. The multicollinearity is caused by some local identification problems in the likelihood function. These same singularities motivate the choice of prior. The proposed method is applied to a dataset of Dutch bond prices.
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by STEFAN THOREN This thesis proposes a way to design software for Monte Carlo simulation that facilitates the simulation of many different kinds of stochastic processes. Monte Carlo simulation is a powerful tool that has applications in many financial contexts. One important application is the pricing of complex financial derivatives. Pricing derivatives is a recurring problem for many financial institutions. Many different kinds of derivatives exist on the financial markets,and new kinds are introduced continually. A software for Monte Carlo simulation that is adaptable to price different derivatives could potentially save money,time and effort. The thesis provides an introduction to Monte Carlo simulation in the financial markets. An analysis of the problem considered in the thesis project is given and a design of a Monte Carlo simulation engine is given. Finally,examples illustrating the use of the software are given.
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by CLAUDIO ALBANESE AND MANLIO TROVATO Abstract. It is widely recognized that fixed income exotics should be priced by means of a stochastic volatility model. Callable constant maturity swaps (CMS) are a particularly interesting case due to the sensitivity of swap rates to implied swaption volatilities for very deep out of the money strikes. In this paper, we introduce a stochastic volatility term structure model based on a continuous time lattice which allows for a numerically stable and quite efficient methodology to price fixed income exotics in this class. Discuss this paper
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by Min Li This paper presents a case study of interest rate term structure estimation of U.S. Treasury bonds and AT&T corporate bonds from April 1994 to December 1995. We first adopt a Bayesian regression spline model to estimate the term structure of risk-free Treasury bonds where the number and location of the spline knots are adaptively selected using the reversible jump Markov chain Monte Carlo algorithm. We then develop a hierarchical Bayesian approach to estimate the corporate term structure, Discuss this paper
The Hull-White model is a single-factor, no arbitrage approach to modeling the term structure of interest rates. It models the term structure by describing the evolution of the short rate, or the instantaneous rate of interest. Implementing this model results in a trinomial pricing tree that can be used to price complex interest rate derivatives such as options on swaps and bonds. The difficulty of this model lies in its relative complexity and multi-stage implementation. The model's advantage over similar models is its calculation speed. This paper does not develop a new method but rather explains the author Discuss this paper
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Is Credit Dead? Value-At-Risk The Origin of Poker, Page 1 and Page 2 Masters of the Poker Bluff The Education of a Poker Player 21st Century Disclosure The Unbearable LIghtness of Cross-Market Risk Monopoly 101, Part I Monopoly 101, Part II What is the Interest Rate in Hell? The Dakota Option Part I The Dakota Option Part II The Dakota Option Part III The Theory of Risk Management Modern Portfolio Theory at Fifty Hedge Fund Risk Management Risk: The Ugly History Time Enough for Counting Ere Your Credit Advance Wald's Series Whose LIfe is it Anyway? A Wall Street Rocket Scientist in King Arthur's Court Table Stakes Six Degrees of Idiocy Discuss this paper
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