scholarly journals Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

2013 ◽  
Vol 45 (2) ◽  
pp. 572-594 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Price Model ◽  
Forward Price ◽  
Volatility Model ◽  
Characteristic Features ◽  
Hump Shape ◽  
Non Gaussian

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

scholarly journals Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

2013 ◽  
Vol 45 (02) ◽  
pp. 572-594 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Price Model ◽  
Forward Price ◽  
Volatility Model ◽  
Characteristic Features ◽  
Hump Shape ◽  
Non Gaussian

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

scholarly journals Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets

2013 ◽  
Vol 45 (02) ◽  
pp. 545-571 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Simulation Method ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Leverage Effect ◽  
Order Structure ◽  
Spot Prices ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility

Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

scholarly journals Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets

2013 ◽  
Vol 45 (2) ◽  
pp. 545-571 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Simulation Method ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Leverage Effect ◽  
Order Structure ◽  
Spot Prices ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility

Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian

scholarly journals MULTISCALE STOCHASTIC VOLATILITY MODEL FOR DERIVATIVES ON FUTURES

2014 ◽  
Vol 17 (07) ◽  
pp. 1450043 ◽  
Author(s):  
JEAN-PIERRE FOUQUE ◽  
YURI F. SAPORITO ◽  
JORGE P. ZUBELLI
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Additional Hypothesis ◽  
First Order ◽  
Volatility Model ◽  
First Order Approximation

In this paper, we present a new method for computing the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility studied in Fouque et al. (2011). It provides an alternative method to the singular perturbation technique presented in Hikspoors & Jaimungal (2008). The main features of our method are twofold: firstly, it does not rely on any additional hypothesis on the regularity of the payoff function, and secondly, it allows an effective and straightforward calibration procedure of the group market parameters to implied volatilities. These features were not achieved in previous works. Moreover, the central argument of our method could be applied to interest rate derivatives and compound derivatives. The only pre-requisite of our approach is the first-order approximation of the underlying derivative. Furthermore, the model proposed here is well-suited for commodities since it incorporates mean reversion of the spot price and multiscale stochastic volatility. Indeed, the model was validated by calibrating the group market parameters to options on crude-oil futures, and it displays a very good fit of the implied volatility.

scholarly journals Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model

2003 ◽  
Vol 23 (2) ◽  
pp. 183
Author(s):  
Anderson C. O. Motta ◽  
Luiz K. Hotta
Keyword(s):  
Maximum Likelihood ◽  
State Space ◽  
Stochastic Volatility ◽  
Stock Exchange ◽  
Estimation Procedure ◽  
Stochastic Volatility Model ◽  
Gaussian State ◽  
Volatility Model ◽  
Non Gaussian ◽  
Exact Maximum Likelihood

This paper considers the classical and Bayesian approaches to the estimation of the stochastic volatility (SV) model. The estimation procedures rely heavily on the fact that SV model can be written in the State Space Form (SSF) with non-Ga ussian disturbances. The first widely employed estimation procedure to use this model was the quasi-maximum likelihood estimator proposed by Harvey et al. The Bayesian approach was proposed by Jacquier et al.(1994). Lately, many papers have appeared in the literature dealing with non-Gaussian state space models which directly influenced the estimation of the SV model. Some of these methods proposed to estimate the SV model are compared using the Sao Paulo stock exchange index (IBOVESPA) and simulated series. The influence of outliers is also considered.

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