The Experts below are selected from a list of 4251 Experts worldwide ranked by ideXlab platform
Nicolas Victoir - One of the best experts on this subject based on the ideXlab platform.
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weak approximation of stochastic differential equations and application to Derivative Pricing
Applied Mathematical Finance, 2008Co-Authors: Syoiti Ninomiya, Nicolas VictoirAbstract:A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of Pricing Asian options under the Heston stochastic volatility model. 2000 Mathematics Subject Classification, 65C30, 65C05.
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Weak approximation of stochastic differential equations and application to Derivative Pricing
Applied Mathematical Finance, 2008Co-Authors: Syoiti Ninomiya, Nicolas VictoirAbstract:The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of Pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasi-Monte Carlo methods makes computations extremely fast. [1] Shigeo Kusuoka, ``Approximation of Expectation of Diffusion Process and Mathematical Finance,'' Advanced Studies in Pure Mathematics, Proceedings of Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp. 147--165. [2] Terry Lyons and Nicolas Victoir, ``Cubature on Wiener Space,'' Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 460 (2004), pp. 169--198.
Syoiti Ninomiya - One of the best experts on this subject based on the ideXlab platform.
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weak approximation of stochastic differential equations and application to Derivative Pricing
Applied Mathematical Finance, 2008Co-Authors: Syoiti Ninomiya, Nicolas VictoirAbstract:A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of Pricing Asian options under the Heston stochastic volatility model. 2000 Mathematics Subject Classification, 65C30, 65C05.
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Weak approximation of stochastic differential equations and application to Derivative Pricing
Applied Mathematical Finance, 2008Co-Authors: Syoiti Ninomiya, Nicolas VictoirAbstract:The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of Pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasi-Monte Carlo methods makes computations extremely fast. [1] Shigeo Kusuoka, ``Approximation of Expectation of Diffusion Process and Mathematical Finance,'' Advanced Studies in Pure Mathematics, Proceedings of Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp. 147--165. [2] Terry Lyons and Nicolas Victoir, ``Cubature on Wiener Space,'' Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 460 (2004), pp. 169--198.
Stephen Jewson - One of the best experts on this subject based on the ideXlab platform.
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weather Derivative Pricing and the normal distribution fitting the variance to maximise expected predictive log likelihood
2006Co-Authors: Stephen Jewson, Jeremy PenzerAbstract:The normal distribution is commonly used to predict weather indices when Pricing weather Derivatives. The standard method for making such predictions involves calculating an unbiased estimator for the population variance. The variance of the prediction (the predictive variance) is then the unbiased estimator for the population variance with an adjustment to account for sampling error on the mean. This is not, however, the only way to model the predictive variance, and it is not necessarily the best way. We investigate an alternative method, based on adjusting the predictive variance so as to maximise the expected predictive log-likelihood. For the small sample sizes often used in weather Derivative Pricing the resulting predictive variances are significantly larger than those calculated using the standard method.
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Weather Derivative Pricing and the Impact of El Nino on US Temperature: Empirical Tests of an Optimal Categorical Forecasting Scheme
SSRN Electronic Journal, 2005Co-Authors: Stephen Jewson, Shree KhareAbstract:Weather Derivative Pricing for US locations can potentially be improved through the judicious use of seasonal forecasts. However, the number of El Nino and La Nina events that appear in the historical record is small and for many locations the signals are weak. We run some simulation-based tests of an optimal categorical forecasting scheme that takes the small sample size and weak signal into account and tries to produce RMSE-optimal seasonal forecasts.
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Weather Derivative Pricing and the Impact of El Nino on US Temperature: The Statistics of Optimal Categorical Predictions
SSRN Electronic Journal, 2005Co-Authors: Stephen Jewson, Jeremy PenzerAbstract:Seasonal forecasts of US temperature have the potential to improve weather Derivative Pricing. One way to produce such forecasts is to divide the range of possible Pacific ocean surface temperatures into three categories and look at the US temperatures that occur for each category. Unfortunately this approach is hampered by weak signals and lack of data. We perform a statistical analysis of this problem and derive expressions for optimal forecasts that take into account the weakness of the signal and the small sample sizes.
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weather Derivative Pricing and a preliminary investigation into a decision rule for detrending
2004Co-Authors: Stephen Jewson, Jeremy PenzerAbstract:Weather Derivative Pricing is often based on year-ahead forecasts of the weather made using simple statistical models and past weather data. Two of the simplest models in common use are the flat line and linear trend models. We consider the question of how to choose between these two models and test a simple decision rule based on closed-form expressions for the RMSE.
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Weather Derivative Pricing and the Interpretation of Linear Trend Models
SSRN Electronic Journal, 2004Co-Authors: Stephen Jewson, Jeremy PenzerAbstract:We interpret the flat line, best fit linear trend and damped linear trend models as a sequence of weights on historical index values. This gives further insight into some of the properties of these models.
Christian Gouriéroux - One of the best experts on this subject based on the ideXlab platform.
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Non-causal Affine Processes with Applications to Derivative Pricing
2020Co-Authors: Christian Gouriéroux, Yang LuAbstract:Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for Pricing sequences of speculative bubbles. We show that they feature much more complicated non affine dynamics in calendar time, while still providing (quasi) closed form term structures and Derivative Pricing formulas. The framework is illustrated with zero-coupon bond and European call option Pricing examples.
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approximate Derivative Pricing for large classes of homogeneous assets with systematic risk
Journal of Financial Econometrics, 2011Co-Authors: Patrick Gagliardini, Christian GouriérouxAbstract:We consider a homogeneous class of assets, whose returns are driven by an unobservable factor representing systematic risk. We derive approximated Pricing formulas for the future factor values and their proxies, when the size n of the class is large. Up to order 1/n, these closed-form approximations involve well-chosen summary statistics of the basic asset returns but not the current and lagged factor values. The potential of the closed-form approximation formulas seems quite large, especially for credit risk analysis, which considers large portfolios of individual loans or corporate bonds, and for longevity risk analysis, which involves large portfolios of life insurance contracts. Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.
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Derivative Pricing with wishart multivariate stochastic volatility
Journal of Business & Economic Statistics, 2010Co-Authors: Christian Gouriéroux, Razvan SufanaAbstract:This paper deals with the Pricing of Derivatives written on several underlying assets or factors satisfying a multivariate model with Wishart stochastic volatility matrix. This multivariate stochastic volatility model leads to a closed-form solution for the conditional Laplace transform, and quasi-explicit solutions for Derivative prices written on more than one asset or underlying factor. Two examples are presented: (i) a multiasset extension of the stochastic volatility model introduced by Heston (1993), and (ii) a model for credit risk analysis that extends the model of Merton (1974) to a framework with stochastic firm liability, stochastic volatility, and several firms. A bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional Laplace transform of the stock returns.
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efficient Derivative Pricing by the extended method of moments
Econometrica, 2005Co-Authors: Patrick Gagliardini, Christian Gouriéroux, Eric RenaultAbstract:In this paper we introduce the Extended Method of Moments (XMM) estimator. This estimator accommodates a more general set of moment restrictions than the standard Generalized Method of Moments (GMM) estimator. More specifically, the XMM differs from the GMM in that it can handle not only uniform conditional moment restrictions (i.e. valid for any value of the conditioning variable), but also local conditional moment restrictions valid for a given fixed value of the conditioning variable. The local conditional moment restrictions are of special relevance in Derivative Pricing for reconstructing the Pricing operator at a given day, by using the information in a few cross-sections of observed traded Derivative prices and a time series of underlying asset returns. The estimated Derivative prices are consistent for large time series dimension, but fixed number of cross-sectionally observed Derivative prices. The asymptotic properties of the XMM estimator are nonstandard, since the combination of uniform and local conditional moment restrictions induces different rates of convergence (parametric and nonparametric) for the parameters.
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Derivative Pricing with multivariate stochastic volatility application to credit risk
2004Co-Authors: Christian Gouriéroux, Razvan SufanaAbstract:This paper extends to the multiasset framework the closed-form solution for options withstochastic volatility derived in Heston (1993) and Ball and Roma (1994). This extensionintroduces a risk premium in the return equation and considers Wishart dynamics for theprocess of the stochastic volatility matrix, which is the multiasset analogue of the model ofCox, Ingersoll, and Ross (1985). This approach is used to extend Merton’s model (Merton(1974)) for corporate default to a framework with stochastic liability, stochastic volatilityand several firms.
Razvan Sufana - One of the best experts on this subject based on the ideXlab platform.
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Derivative Pricing with wishart multivariate stochastic volatility
Journal of Business & Economic Statistics, 2010Co-Authors: Christian Gouriéroux, Razvan SufanaAbstract:This paper deals with the Pricing of Derivatives written on several underlying assets or factors satisfying a multivariate model with Wishart stochastic volatility matrix. This multivariate stochastic volatility model leads to a closed-form solution for the conditional Laplace transform, and quasi-explicit solutions for Derivative prices written on more than one asset or underlying factor. Two examples are presented: (i) a multiasset extension of the stochastic volatility model introduced by Heston (1993), and (ii) a model for credit risk analysis that extends the model of Merton (1974) to a framework with stochastic firm liability, stochastic volatility, and several firms. A bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional Laplace transform of the stock returns.
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Derivative Pricing with multivariate stochastic volatility application to credit risk
2004Co-Authors: Christian Gouriéroux, Razvan SufanaAbstract:This paper extends to the multiasset framework the closed-form solution for options withstochastic volatility derived in Heston (1993) and Ball and Roma (1994). This extensionintroduces a risk premium in the return equation and considers Wishart dynamics for theprocess of the stochastic volatility matrix, which is the multiasset analogue of the model ofCox, Ingersoll, and Ross (1985). This approach is used to extend Merton’s model (Merton(1974)) for corporate default to a framework with stochastic liability, stochastic volatilityand several firms.