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20
Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
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Cited by 149 (2 self)
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes
, 1999
"... Introduction and motivation The problem of how to specify a correlation matrix occurs in several important areas of finance and of risk management. A few of the important applications are, for instance, the specification of a (possibly timedependent) instantaneous correlation matrix in the context ..."
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Cited by 38 (0 self)
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Introduction and motivation The problem of how to specify a correlation matrix occurs in several important areas of finance and of risk management. A few of the important applications are, for instance, the specification of a (possibly timedependent) instantaneous correlation matrix in the context of the BGM interestrate option models, stresstesting and scenario analysis for market risk management purposes, or the specification of a correlation matrix amongst a large number of obligors for creditderivative pricing or credit risk management. For those applications where the most important desideratum is the recovery of the realworld correlation matrix, the problem is in principle well defined and readily solvable by means of wellestablished statistical techniques. In practice, however, the estimation problems can be severe: a small number of outliers, for instance, can seriously "pollute" a sample; nonsynchronous data can easily destroy or hide correlation
Dynamics of Implied Volatility Surfaces.
, 2001
"... The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. ..."
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Cited by 11 (0 self)
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The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce.
Linking Caplet and Swaption Volatilities in a BGM/J Framework: Approximate Solutions
 QUARC, Royal Bank of
, 2000
"... We present and approximation for the volatility of European swaptions in a forward rate based BraceGatarekMusiela/Jamshidian framework [BGM97, Jam97] which enables us to calculate prices for swaptions without the need for Monte Carlo simulations. Also, we explain the mechanism behind the remarkabl ..."
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Cited by 6 (1 self)
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We present and approximation for the volatility of European swaptions in a forward rate based BraceGatarekMusiela/Jamshidian framework [BGM97, Jam97] which enables us to calculate prices for swaptions without the need for Monte Carlo simulations. Also, we explain the mechanism behind the remarkable accuracy of these approximate prices. For cases where the yield curve varies noticeably as a function of maturity, a second, and even more accurate formula is derived. 1
Bounding Bermudan Swaptions In A SwapRate Market Model
 Quantitative Finance
, 2002
"... We develop a new method for finding upper bounds for Bermudan swaptions in a swaprate market model. By comparing with lower bounds found by exercise boundary parametrization, we find that the bounds are well within bido#er spread. As an application, we study the dependence of Bermudan swaption ..."
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Cited by 6 (0 self)
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We develop a new method for finding upper bounds for Bermudan swaptions in a swaprate market model. By comparing with lower bounds found by exercise boundary parametrization, we find that the bounds are well within bido#er spread. As an application, we study the dependence of Bermudan swaption prices on the number of instantaneous factors used in the model.
An EZI method to reduce the rank of a correlation matrix in financial modelling
 Appl. Math. Finance
, 2006
"... To link to this Article: DOI: 10.1080/13504860600658976 ..."
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Cited by 6 (0 self)
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To link to this Article: DOI: 10.1080/13504860600658976
A Note on Correlation and Rank Reduction ∗
"... We review both fullrank and reducedrank parameterizations for correlation matrices. In particular, the fullrank parameterizations of Rebonato (1999d) and Schoenmakers and Coffey (2000), the reducedrank angle parameterization of Rebonato (1999d) and Rebonato and Jäckel (1999), and the well known ..."
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Cited by 3 (0 self)
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We review both fullrank and reducedrank parameterizations for correlation matrices. In particular, the fullrank parameterizations of Rebonato (1999d) and Schoenmakers and Coffey (2000), the reducedrank angle parameterization of Rebonato (1999d) and Rebonato and Jäckel (1999), and the well known zeroedeigenvalues reducedrank approximation are described in detail. Numerical examples are provided for the reducedrank parameterizations and results are compared. 1
Valuing American options in the presence of userdefined smiles and timedependent volatility: scenario analysis, model stress and lowerbound pricing applications.
, 2000
"... A method is presented for the valuation of American style options as a function of an exogeneosly assigned future implied volatility surface. Subject to this specification, this is done independently of any assumptions about a stochastic process of the underlying asset. ..."
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A method is presented for the valuation of American style options as a function of an exogeneosly assigned future implied volatility surface. Subject to this specification, this is done independently of any assumptions about a stochastic process of the underlying asset.
The Volatility Smile Dynamics Implied by SmileConsistent Option Pricing Models and Empirical Data
, 2008
"... It is wellknown that the fair value of options can be determined by using the BlackScholes model. However, for liquidly traded options, i.e. instruments for which the market price is known, there is clear evidence that the BlackScholes model is not correct. This is reflected in the existence of t ..."
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It is wellknown that the fair value of options can be determined by using the BlackScholes model. However, for liquidly traded options, i.e. instruments for which the market price is known, there is clear evidence that the BlackScholes model is not correct. This is reflected in the existence of the volatility smile phenomenon which is one the most challenging problems in financial economics. Recently, a rigorous analysis of the time evolution of the empirically observed volatility smile, i.e. smile dynamics, has been reported by (CdF02) and (Fen05). However, the quantification of the volatility smile dynamics as implied by smileconsistent models has not been done rigorously, so far. People have addressed this by looking at the evolution of the smile, based on asymptotic analysis and qualitative investigations. In this work, we use similar statistical techniques as employed in the empirical studies, to quantify the smile dynamics that is implied by the following smileconsistent models: Displaced Diffusion, Constant Elasticity of Variance (CEV) and SABR Stochastic Volatility Models. We find that in markets where options exhibit extreme skew, e.g. equity options markets, the displaced diffusion and CEV models should be used with care, since these models have poor fitting capabilities to market prices and impose inaccurate smile dynamics. The SABR model on the other
Systems and Operations Research Strategy and International Business
"... This thesis develops a method for market risk measurement of an interest rate derivatives portfolio. The potential value loss of the portfolio is tested on a daily basis using market scenarios for interest rates and interest rate volatilities. Test scenarios are chosen to represent plausible changes ..."
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This thesis develops a method for market risk measurement of an interest rate derivatives portfolio. The potential value loss of the portfolio is tested on a daily basis using market scenarios for interest rates and interest rate volatilities. Test scenarios are chosen to represent plausible changes in the market factors. The portfolio being tested consists of interest rate instruments including swaps, forward rate agreements, futures contracts, futures options, interest rate caps and floors and swaptions. Valuation models for these instrument types are introduced. The market scenarios are specified from historical interest rate data using principal components analysis. The resulting principal components are interpreted as typical market movements and are therefore chosen as test scenarios. Scenarios testing is used as a supplementary market risk measurement tool in conjunction with the incumbent risk management tools. It is found that the risk measures that result from the test scenarios do help the dealers and the risk managers to evaluate the structure of the current derivatives position. However, the benefits over the current risk measures are limited, and better results could be obtained by methods like scenario simulation and Value at Risk.