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74
The JumpRisk Premia Implicit in Options: Evidence from an Integrated TimeSeries Study
 Journal of Financial Economics
"... Abstract: This paper examines the joint time series of the S&P 500 index and nearthemoney shortdated option prices with an arbitragefree model, capturing both stochastic volatility and jumps. Jumprisk premia uncovered from the joint data respond quickly to market volatility, becoming more p ..."
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Cited by 369 (2 self)
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Abstract: This paper examines the joint time series of the S&P 500 index and nearthemoney shortdated option prices with an arbitragefree model, capturing both stochastic volatility and jumps. Jumprisk premia uncovered from the joint data respond quickly to market volatility, becoming more prominent during volatile markets. This form of jumprisk premia is important not only in reconciling the dynamics implied by the joint data, but also in explaining the volatility “smirks” of crosssectional options data.
A Study towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation
, 1999
"... The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundame ..."
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Cited by 116 (4 self)
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The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price S t and a set of option contracts ### I it # i=1;m # where m # 1 and # I it is the BlackScholes implied volatility.We use Heston's #1993# model as an example and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. Abyproduct of this #nding is that we uncover a remarkably simple volatility extraction #lter based on a polynomial lag structure of implied volatilities. The bivariate approachinvolving both the fundamental and an option appears useful when the information from the cash market ...
Estimation of stochastic volatility models via Monte Carlo Maximum Likelihood
, 1998
"... This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chisquare disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it int ..."
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Cited by 98 (9 self)
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This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chisquare disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.
Complete Models with Stochastic Volatility
, 1996
"... The paper proposes an original class of models for the continuous time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentiallyweighted moments of historic logprice. The instantaneous volatility is therefore driven ..."
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Cited by 73 (4 self)
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The paper proposes an original class of models for the continuous time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentiallyweighted moments of historic logprice. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preferenceindependent options prices. We find a partial differential equation for the price of a European Call Option. Smiles and skews are found in the resulting plots of implied volatility. Keywords: Option pricing, stochastic volatility, complete markets, smiles. Acknowledgement. It is a pleasure to thank the referees of an earlier draft of this paper whose perceptive comments have resulted in many improvements. 1 Research supported in part by Record Treasu...
Derivative asset analysis in models with leveldependent and stochastic volatility
 CWI QUARTERLY
, 1996
"... In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope wit ..."
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Cited by 52 (1 self)
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In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope with the known deficits of the classical BlackScholes model. We start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the classical BlackScholes model. After a review of the known empirical contradictions to the classical BlackScholes model we consider models with leveldependent volatility. Most of this survey is devoted to derivative asset analysis in stochastic volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context of stochastic volatility models and review analytical and numerical approaches to the actual computation of option values.
MeanReverting Stochastic Volatility
, 2000
"... We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis of highfrequency S&P 500 index data confirms that volatility reverts slowly to its me ..."
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Cited by 35 (9 self)
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We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis of highfrequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparison to the tickbytick fluctuations of the index value, but it is fast meanreverting when looked at over the time scale of a derivative contract (many months). This motivates an asymptotic analysis of the partial differential equation satisfied by derivative prices, utilizing the distinction between these time scales. The analysis yields pricing and implied volatility formulas, and the latter is used to "fit the smile" from European index option prices. The theory identifies the important group parameters that are needed for the derivative pricing and hedging problem for Europeanstyle securities, namely the average volatility and the slope and intercept of the implied volatility line, plotted as a function of the logmoneynesstomaturityratio. The results considerably simplify the estimation procedure, and the data produces estimates
General BlackScholes models accounting for increased market volatility from hedging strategies
, 1997
"... Increases in market volatility of asset prices have been observed and analyzed in recent years and their cause has generally been attributed to the popularity of portfolio insurance strategies for derivative securities. The basis of derivative pricing is the BlackScholes model and its use is so ext ..."
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Cited by 34 (1 self)
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Increases in market volatility of asset prices have been observed and analyzed in recent years and their cause has generally been attributed to the popularity of portfolio insurance strategies for derivative securities. The basis of derivative pricing is the BlackScholes model and its use is so extensive that it is likely to influence the market itself. In particular it has been suggested that this is a factor in the rise in volatilities. In this work we present a class of pricing models that account for the feedback effect from the BlackScholes dynamic hedging strategies on the price of the asset, and from there back onto the price of the derivative. These models do predict increased implied volatilities with minimal assumptions beyond those of the BlackScholes theory. They are characterized by a nonlinear partial differential equation that reduces to the BlackScholes equation when the feedback is removed. We begin with a model economy consisting of two distinct groups of traders: Reference traders who are the majority investing in the asset expecting gain, and program traders who trade the asset following a BlackScholes type dynamic hedging strategy, which is not known a priori, in order to insure against the risk of a derivative security. The interaction of these groups leads to a stochastic process for the price of the asset which depends on the hedging strategy of the program traders. Then following a BlackScholes argument, we
Closedform solutions for perpetual American Put options with regime switching
 SIAM Journal on Applied Mathematics
"... Abstract. This paper studies an optimal stopping time problem for pricing perpetual American put options in a regime switching model. An explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the “modified smooth fit ” technique. The solution is then ..."
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Cited by 33 (1 self)
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Abstract. This paper studies an optimal stopping time problem for pricing perpetual American put options in a regime switching model. An explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the “modified smooth fit ” technique. The solution is then compared with the numerical results obtained via a dynamic programming approach and also with a twopoint boundaryvalue differential equation (TPBVDE) method. Key words. Markov chain, optimal stopping time, American options, regime switching, modified smooth fit principle AMS subject classifications. 90A09, 60J27 DOI. 10.1137/S0036139903426083 1. Introduction. Given a probability space (Ω, F,P), consider a process X(t) which satisfies (in a strong sense) a stochastic differential equation of the following form: (1) dX(t)=X(t)µ ɛ(t)dt + X(t)σ ɛ(t)dW(t), X(0) = x,
Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk
, 2005
"... We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of e ..."
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Cited by 32 (6 self)
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We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) The jump and endogenous default can produce a variety of nonzero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The twosided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; and although in generel credit spreads and implied volatility tend to move in the same direction under exogenous default models, but this may not be true in presence of endogenous default and jumps. In terms of mathematical contribution, we give a proof of a version of the “smooth fitting ” principle for the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model. 1
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 24 (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.