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209
Option Pricing by Transform Methods: Extensions, Unification, and Error Control
- Journal of Computational Finance
"... We extend and unify Fourier-analytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorith ..."
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Cited by 89 (6 self)
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We extend and unify Fourier-analytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorithms to select efficient quadrature parameters and to price with guaranteed numerical accuracy.
Stochastic volatility with leverage: fast likelihood inference
- Journal of Econometrics
, 2007
"... Kim, Shephard, and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which is known to be important in applications. Despite this, their basic method has been ex ..."
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Cited by 68 (19 self)
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Kim, Shephard, and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which is known to be important in applications. Despite this, their basic method has been extensively used in the financial economics literature and more recently in macroeconometrics. In this paper we show how the basic approach can be extended in a novel way to stochastic volatility models with leverage without altering the essence of the original approach. Several illustrative examples are provided.
Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes
, 2003
"... We analyze the specifications of option pricing models based on time-changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. O ..."
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Cited by 67 (12 self)
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We analyze the specifications of option pricing models based on time-changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we must incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component.
Variation, jumps, market frictions and high frequency data in financial econometrics
, 2005
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Maximum likelihood estimation of latent affine processes, Working paper
- Processes, forthcoming, Review of Financial Studies
, 2006
"... This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes ’ rule for recursively updating the joint cha ..."
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Cited by 48 (2 self)
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This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes ’ rule for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. An application to daily stock market returns over 1953-96 reveals substantial divergences from EMM-based estimates; in particular, more substantial and time-varying jump risk. The implications for pricing stock index options are examined. 3 “The Lion in Affrik and the Bear in Sarmatia are Fierce, but Translated into a Contrary Heaven, are of less Strength and Courage.” Jacob Ziegler; translated by Richard Eden (1555) While models proposing time-varying volatility of asset returns have been around for thirty years, it has proven extraordinarily difficult to estimate the parameters of the underlying volatility process,
Pricing American Options Under Variance
- Gamma, J. Comp. Finance
"... We derive a form of the partial integro-differential equation (PIDE) for pricing American options under variance gamma (VG) process. We then develop a numerical algorithm to solve for values of American options under variance gamma model. In this study, we compare the exercise boundary and early exe ..."
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Cited by 47 (2 self)
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We derive a form of the partial integro-differential equation (PIDE) for pricing American options under variance gamma (VG) process. We then develop a numerical algorithm to solve for values of American options under variance gamma model. In this study, we compare the exercise boundary and early exercise premia between geo-metric VG law and geometric Brownian motion (GBM). We find that GBM premia are understated and hence we conclude that further work is necessary in developing fast efficient algorithms for solving PIDE’s with a view to calibrating stochastic processes to a surface of American option prices. 1
Meromorphic Lévy processes and their fluctuation identities
- Annals of Applied Probability
, 2011
"... The last couple of years has seen a remarkable number of new, explicit examples of the Wiener–Hopf factorization for Lévy processes where previously there had been very few. We mention, in particular, the many cases of spectrally negative Lévy processes in [Sixth Seminar on Stochastic Analysis, ..."
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Cited by 37 (10 self)
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The last couple of years has seen a remarkable number of new, explicit examples of the Wiener–Hopf factorization for Lévy processes where previously there had been very few. We mention, in particular, the many cases of spectrally negative Lévy processes in [Sixth Seminar on Stochastic Analysis,
Analysis of Fourier transform valuation formulas and applications
- Applied Mathematical Finance
"... Abstract. The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the ..."
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Cited by 35 (9 self)
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Abstract. The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in Lévy and stochastic volatility models.
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
- J. Eur. Math. Soc. (JEMS
"... Abstract. This paper is concerned with Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the clas ..."
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Cited by 31 (4 self)
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Abstract. This paper is concerned with Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on x and also a large class of equations, including Bellman-Isaacs Equations.
