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802
Pricing with a Smile
 Risk Magazine
, 1994
"... prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the same for all option market prices, but reality shows this is not the case. Implied Black–Scholes vol ..."
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Cited by 445 (1 self)
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prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the same for all option market prices, but reality shows this is not the case. Implied Black
Testing ContinuousTime Models of the Spot Interest Rate
 Review of Financial Studies
, 1996
"... Different continuoustime models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuoustime model by discrete approximations, even though the data are rec ..."
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Cited by 310 (9 self)
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are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then meanreverts strongly when far away from the mean. The volatility
Intertemporally dependent preferences and the volatility of consumption and wealth
 Review of Financial Studies
, 1989
"... In this article we construct a model in which a consumer’s utility depends on the consumption history We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closedform in this general equilibrium setting to rationalize the observed ..."
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Cited by 168 (3 self)
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Breeden, Michael Brennan, John Cox, Chifu Huang, and Krishna Ramaswamy for their thoughtful comments and criticisms. I also thank Tongsheng Sun for explaining the simulation procedure for stochastic differential equations and for his comments and suggestions. I am responsible for any remaining errors
Exact Simulation of Stochastic Volatility and other
 Affine Jump Diffusion Processes, Working Paper
, 2004
"... The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introduces bias into the simulation results and a large nu ..."
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Cited by 123 (1 self)
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The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introduces bias into the simulation results and a large
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 76 (4 self)
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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
Penalty Methods For American Options With Stochastic Volatility
, 1998
"... The American early exercise constraint can be viewed as transforming the two dimensional stochastic volatility option pricing PDE into a differential algebraic equation (DAE). Several methods are described for forcing the algebraic constraint by using a penalty source term in the discrete equations. ..."
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Cited by 100 (20 self)
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The American early exercise constraint can be viewed as transforming the two dimensional stochastic volatility option pricing PDE into a differential algebraic equation (DAE). Several methods are described for forcing the algebraic constraint by using a penalty source term in the discrete equations
Localizing volatilities
, 2004
"... We propose two main applications of Gyöngy (1986)’s construction of inhomogeneous Markovian stochastic differential equations that mimick the onedimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)’s result. We then present Besselbased stoch ..."
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Cited by 4 (0 self)
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We propose two main applications of Gyöngy (1986)’s construction of inhomogeneous Markovian stochastic differential equations that mimick the onedimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)’s result. We then present Bessel
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 40 (10 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
Managing The Volatility Risk Of Portfolios Of Derivative Securities: The Lagrangian Uncertain Volatility Model
 Applied Mathematical Finance
, 1996
"... We present an algorithm for hedging option portfolios and customtailored derivative securities which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a nonlinear partial differential equation to evaluate worstcase volatility scenarios fo ..."
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Cited by 51 (5 self)
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We present an algorithm for hedging option portfolios and customtailored derivative securities which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a nonlinear partial differential equation to evaluate worstcase volatility scenarios
Asymptotics and calibration of local volatility models
 Quant. Finance
"... We derive a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation. Using this equation we establish closedform asymptotic formulae for the implied volatility near expiry as well as for deep in and outofthemoney options ..."
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Cited by 50 (1 self)
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We derive a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation. Using this equation we establish closedform asymptotic formulae for the implied volatility near expiry as well as for deep in and out
Results 1  10
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802