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22
Do stock prices and volatility jump? Reconciling evidence from spot and option prices
, 2001
"... This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation ..."
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Cited by 97 (2 self)
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This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation period. This contrasts previous findings where stochastic volatility paths are found to be too smooth relative to the option implied dynamics. While the models perform well during the high volatility estimation period, they tend to overprice long dated contracts outofsample. This evidence points towards a too simplistic specification of the mean dynamics of volatility.
Model uncertainty and its impact on the pricing of derivative instruments
 Mathematical Finance
"... Uncertainty on the choice of an option pricing model can lead to “model risk ” in the valuation of portfolios of options. After discussing some properties which a quantitative measure of model uncertainty should verify in order to be useful and relevant in the context of risk management of derivativ ..."
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Cited by 30 (6 self)
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Uncertainty on the choice of an option pricing model can lead to “model risk ” in the valuation of portfolios of options. After discussing some properties which a quantitative measure of model uncertainty should verify in order to be useful and relevant in the context of risk management of derivative instruments, we introduce a quantitative framework for measuring model uncertainty in the context of derivative pricing. Two methods are proposed: the first method is based on a coherent risk measure compatible with market prices of derivatives, while the second method is based on a convex risk measure. Our measures of model risk lead to a premium for model uncertainty which is comparable to other risk measures and compatible with observations of market prices of a set of benchmark derivatives. Finally, we discuss some implications for the management of “model risk.”
MCMC methods for continuoustime financial econometrics

, 2003
"... This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuoustime 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 explor ..."
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Cited by 24 (1 self)
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This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuoustime 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 highdimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the CliffordHammersley theorem, the Gibbs sampler, the MetropolisHastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuoustime asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regimeswitching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.
Nonparametric Option Pricing by Transformation
, 2002
"... This paper develops a nonparametric option pricing theory and numerical method for European, American and pathdependent derivatives. In contrast to the nonparametric curve fitting techniques commonly seen in the literature, this nonparametric pricing theory is more in line with the canonical val ..."
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Cited by 6 (1 self)
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This paper develops a nonparametric option pricing theory and numerical method for European, American and pathdependent derivatives. In contrast to the nonparametric curve fitting techniques commonly seen in the literature, this nonparametric pricing theory is more in line with the canonical valuation method developed Stutzer (1996) for pricing options with only a sample of asset returns. Unlike the canonical valuation method, however, our nonparametric pricing theory characterizes the asset price behavior periodbyperiod and hence is able to price European, American and pathdependent derivatives. This nonparametric theory relies on transformation to normality and can deal with asset returns that are either i.i.d. or dynamic. Applications to simulated and real data are provided and implications discussed.
BAYESIAN OPTION PRICING USING MIXED NORMAL HETEROSKEDASTICITY MODELS
, 2009
"... While stochastic volatility models improve on the option pricing error when compared to the BlackScholesMerton model, mispricings remain. This paper uses mixed normal heteroskedasticity models to price options. Our model allows for significant negative skewness and time varying higher order moment ..."
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Cited by 6 (2 self)
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While stochastic volatility models improve on the option pricing error when compared to the BlackScholesMerton model, mispricings remain. This paper uses mixed normal heteroskedasticity models to price options. Our model allows for significant negative skewness and time varying higher order moments of the risk neutral distribution. Parameter inference using Gibbs sampling is explained and we detail how to compute risk neutral predictive densities taking into account parameter uncertainty. When forecasting outofsample options on the S&P 500 index, substantial improvements are found compared to a benchmark model in terms of dollar losses and the ability to explain the smirk in implied volatilities.
The Importance of the Loss Function in Option Pricing
, 2001
"... Which loss function should be used when estimating and evaluating option pricing models? Many different functions have been suggested, but no standard has emerged. We do not promote a particular function, but instead emphasize that consistency in the choice of loss functions is crucial. First, for a ..."
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Cited by 4 (0 self)
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Which loss function should be used when estimating and evaluating option pricing models? Many different functions have been suggested, but no standard has emerged. We do not promote a particular function, but instead emphasize that consistency in the choice of loss functions is crucial. First, for any given model, the loss function used in parameter estimation and model evaluation should be identical, otherwise suboptimal parameter estimates will be obtained. Second, when comparing models, the estimation loss function should be identical across models, otherwise unfair comparisons will be made. We illustrate the importance of these issues in an application of the socalled Practitioner BlackScholes (PBS) model to S&P500 index options. We find reductions of over 50 percent in the root mean squared error of the PBS model when the estimation and evaluation loss functions are aligned. We also find that the PBS model outperforms a benchmark structural model when the estimation loss functions are identical across models, but otherwise not. The new PBS model with aligned loss functions thus represents a much tougher benchmark against which future structural models can be compared.
A Bayesian Approach to Financial Model Calibration, Uncertainty Measures and Optimal Hedging
"... Michaelmas 2009This thesis is dedicated to the late ..."
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Cited by 1 (1 self)
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Michaelmas 2009This thesis is dedicated to the late
Robust Calibration of Financial Models Using Bayesian Estimators
, 2012
"... We consider a general calibration problem for derivative pricing models, which we reformulate into a Bayesian framework to attain posterior distributions for model parameters. It is then shown how the posterior distribution can be used to estimate prices for exotic options. We apply the procedure to ..."
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Cited by 1 (1 self)
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We consider a general calibration problem for derivative pricing models, which we reformulate into a Bayesian framework to attain posterior distributions for model parameters. It is then shown how the posterior distribution can be used to estimate prices for exotic options. We apply the procedure to a discrete local volatility model and work in great detail through numerical examples to clarify the construction of Bayesian estimators and their robustness to the model specification, number of calibration products, noisy data and misspecification of the prior. 1
Model uncertainty and its impact on derivative pricing
 Rethinking Risk Management and Reporting: Uncertainty, Bayesian Analysis and Expert Judgement. Risk Books
, 2010
"... Financial derivatives written on an underlying can normally be priced and hedged accurately only after a suitable mathematical model for the underlying has been determined. This chapter explains the difficulties in finding a (unique) realistic model — model uncertainty. If the wrong model is chosen ..."
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Cited by 1 (1 self)
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Financial derivatives written on an underlying can normally be priced and hedged accurately only after a suitable mathematical model for the underlying has been determined. This chapter explains the difficulties in finding a (unique) realistic model — model uncertainty. If the wrong model is chosen
The Effect Of MisEstimating Correlation On Calculating ValueAtRisk
 Forthcoming in the Journal of Risk Finance
"... This paper examines the systematic relationship between correlation misestimation and the corresponding ValueatRisk (VaR) miscalculation. To this end, first a semiparametric approach, and then a parametric approach is developed. Both approaches are based on a simulation setup. Various linear an ..."
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This paper examines the systematic relationship between correlation misestimation and the corresponding ValueatRisk (VaR) miscalculation. To this end, first a semiparametric approach, and then a parametric approach is developed. Both approaches are based on a simulation setup. Various linear and nonlinear portfolios are considered, as well as variancecovariance and MonteCarlo simulation methods are employed. We find that the VaR error increases significantly as the correlation error increases, particularly in the case of welldiversified linear portfolios. In the case of option portfolios, this effect is more pronounced for shortmaturity, inthemoney options. The use of MC simulation to calculate VaR magnifies the correlation bias effect. Our results have important implications for measuring market risk accurately.