Results 1  10
of
25
Modeling correlated defaults: First passage model under stochastic volatility
 Journal of Computational Finance
, 2006
"... Default dependency structure is crucial in pricing multiname credit derivatives as well as in credit risk management. In this paper, we extend the first passage model for one name with stochastic volatility (FouqueSircarSølna, Applied Mathematical Finance 2006) to the multiname case. Correlation ..."
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Cited by 13 (5 self)
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Default dependency structure is crucial in pricing multiname credit derivatives as well as in credit risk management. In this paper, we extend the first passage model for one name with stochastic volatility (FouqueSircarSølna, Applied Mathematical Finance 2006) to the multiname case. Correlation of defaults is generated by correlation between the Brownian motions driving the individual names as well as through common stochastic volatility factors. A numerical example for the loss distribution of a portfolio of defaultable bonds is examined after stochastic volatility is incorporated. 1
MCMC estimation of multiscale stochastic volatility models
 In Handbook of Quantitative Finance and Risk
, 2009
"... In this paper we propose to use Monte Carlo Markov Chain methods to estimate the parameters of Stochastic Volatility Models with several factors varying at different time scales. The originality of our approach, in contrast with classical factor models is the identification of two factors driving un ..."
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Cited by 6 (3 self)
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In this paper we propose to use Monte Carlo Markov Chain methods to estimate the parameters of Stochastic Volatility Models with several factors varying at different time scales. The originality of our approach, in contrast with classical factor models is the identification of two factors driving univariate series at wellseparated time scales. This is tested with simulated data as well as foreign exchange data.
Multiname and multiscale default modeling
, 2008
"... Multiname default modeling is crucial in the context of pricing credit derivatives such as Collaterized Debt Obligations (CDOs). We consider here a simple reduced form approach for multiname defaults based on the Vasicek or OrnsteinUhlenbeck model for the hazard rates of the underlying names. We an ..."
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Cited by 3 (2 self)
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Multiname default modeling is crucial in the context of pricing credit derivatives such as Collaterized Debt Obligations (CDOs). We consider here a simple reduced form approach for multiname defaults based on the Vasicek or OrnsteinUhlenbeck model for the hazard rates of the underlying names. We analyze the impact of volatility time scales on the default distribution and CDO prices. We demonstrate how correlated fluctuations in the parameters of the name hazard rates affect the loss distribution and senior tranches of CDOs. The effect of stochastic parameter fluctuations is to change the shape of the loss distribution and cannot be captured by using averaged parameters in the original model. Our analysis assumes a separation of time scales and leads to a singularregular perturbation problem [7, 8]. This framework allows us to compute perturbation approximations that can be used for effective pricing of CDOs. 1
Pricing options on defaultable stocks
, 2008
"... We develop stock option price approximations for a model which takes both the risk of default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it might be possible to infer the risk neutral default intensity from the stoc ..."
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Cited by 3 (1 self)
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We develop stock option price approximations for a model which takes both the risk of default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it might be possible to infer the risk neutral default intensity from the stock option prices. Our option price approximation has a rich implied volatility surface structure and fits the data implied volatility well. Our calibration exercise shows that an effective hazard rate from bonds issued by a company can be used to explain the implied volatility skew of the option prices issued by the same company. We also observe that the implied yield spread that is obtained from calibrating all the model parameters to the option prices matches the observed yield spread.
SMALLTIME ASYMPTOTICS FOR FAST MEANREVERTING STOCHASTIC VOLATILITY MODELS ∗
, 1009
"... In this paper, we study stochastic volatility models in regimes where thematurityis small butlarge compared tothemeanreversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB type equations where the “fast variable ” li ..."
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Cited by 3 (0 self)
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In this paper, we study stochastic volatility models in regimes where thematurityis small butlarge compared tothemeanreversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB type equations where the “fast variable ” lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle and we deduce asymptotic prices for OutofTheMoney call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in [11] (J. Feng, M. Forde and J.P. Fouque, Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model, SIAM Journal on Financial Mathematics, Vol. 1, 2010) by a moment generating function computation in the particular case of the Heston model.
Volatility models: from garch to multihorizon cascades
 Financial Markets and the Global Recession. Nova Science Publishers Inc, NY (forthcoming
, 2010
"... We overview different methods of modeling stock prices and exchange rates volatility, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of volatility change across the time scales of observations. Adequacy of volatility models for descri ..."
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Cited by 3 (2 self)
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We overview different methods of modeling stock prices and exchange rates volatility, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of volatility change across the time scales of observations. Adequacy of volatility models for describe price dynamics at several time horizons simultaneously Special attention is a central topic of this study. We propose a detailed survey of recent volatility models, accounting for multiple horizons. These models are based on different and sometimes competing theoretical concepts, belonging either to GARCH or stochastic family of models and often borrowing methodological tools from statistical physics. We compare their properties and comment on their practical usefulness and perspectives.
Timing the Smile
, 2003
"... Within the general framework of stochastic volatility, the authors propose a method, which is consistent with noarbitrage, to price complicated pathdependent derivatives using only the information contained in the implied volatility skew. This method exploits the time scale content of volatility t ..."
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Cited by 2 (1 self)
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Within the general framework of stochastic volatility, the authors propose a method, which is consistent with noarbitrage, to price complicated pathdependent derivatives using only the information contained in the implied volatility skew. This method exploits the time scale content of volatility to bridge the gap between skews and derivatives prices. Here they present their pricing formulas in terms of Greeks free from the details of the underlying models and mathematical techniques. 1 Underlying or Smile? Our goal is to address the following fundamental question in pricing and hedging derivatives. How traded call options, quoted in terms of implied volatilities, can be used to price and hedge more complicated contracts. One
MULTISCALE TIMECHANGED BIRTH PROCESSES FOR PRICING MULTINAME CREDIT DERIVATIVES
"... Abstract. We develop two parsimonious models for pricing multiname credit derivatives. We derive closed form expression for the loss distribution, which then can be used in determining the prices of tranche and index swaps and more exotic derivatives on these contracts. Our starting point is the mo ..."
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Cited by 2 (0 self)
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Abstract. We develop two parsimonious models for pricing multiname credit derivatives. We derive closed form expression for the loss distribution, which then can be used in determining the prices of tranche and index swaps and more exotic derivatives on these contracts. Our starting point is the model of [2], which takes the loss process as a time changed birth process. We introduce stochastic parameter variations into the intensity of the loss process and use the multitime scale approach of [4] and obtain explicit perturbation approximations to the loss distribution. We demonstrate the competence of our approach by calibrating it to the CDX index data. 1.
Convergence by viscosity methods in multiscale financial models with stochastic volatility
 SIAM J. Finan. Math
"... Abstract. We study singular perturbations of a class of stochastic control problems under assumptions motivated by models of financial markets with stochastic volatilities evolving on a fast time scale. We prove the convergence of the value function to the solution of a limit (effective) Cauchy prob ..."
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Cited by 2 (2 self)
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Abstract. We study singular perturbations of a class of stochastic control problems under assumptions motivated by models of financial markets with stochastic volatilities evolving on a fast time scale. We prove the convergence of the value function to the solution of a limit (effective) Cauchy problem for a parabolic equation of HamiltonJacobiBellman type. We use methods of the theory of viscosity solutions and of the homogenization of fully nonlinear PDEs. We test the result on some financial examples, such as Merton portfolio optimization problem. Key words. Singular perturbations, viscosity solutions, stochastic volatility, asymptotic approximation, portfolio optimization. AMS subject classifications. 35B25, 91B28, 93C70, 49L25.