A Unified Stochastic Volatility - Stochastic Correlation Model

2020 ◽  
Author(s):  
Gunter A. Meissner ◽  
Hong Sherwin
Keyword(s):  
Stochastic Volatility ◽  
Correlation Model ◽  
Stochastic Correlation

scholarly journals A Unified Stochastic Volatility—Stochastic Correlation Model

2020 ◽  
Vol 10 (04) ◽  
pp. 679-696
Author(s):  
Xiang Lu ◽  
Gunter Meissner ◽  
Hong Sherwin
Keyword(s):  
Stochastic Volatility ◽  
Correlation Model ◽  
Stochastic Correlation

WORST-OF OPTIONS AND CORRELATION SKEW UNDER A STOCHASTIC CORRELATION FRAMEWORK

2012 ◽  
Vol 15 (07) ◽  
pp. 1250051 ◽  
Author(s):  
JACINTO MARABEL ROMO
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Term Structure ◽  
Stochastic Volatility Model ◽  
Closed Form Solutions ◽  
Stochastic Correlation ◽  
Term Structures ◽  
Volatility Model ◽  
Wide Range ◽  
Correlation Term

This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the underlying assets, as well as between their volatilities. The model accounts for the existence of correlation term structure and correlation skew. The article shows that the Wishart specification can generate different patterns corresponding to the correlation skew for a wide range of correlation term structures. Another advantage of the model is that it is analytically tractable and, hence, it is possible to obtain semi-closed-form solutions for the prices of plain vanilla options, as well as for the price of exotic derivatives. In this sense, this article develops semi-closed-form formulas for the price of European worst-of options with barriers and/or forward-start features. To motivate the introduction of the Wishart volatility model, the article compares the prices obtained under this model and under a multi-asset stochastic volatility model with constant instantaneous correlations. The results reveal the existence of a stochastic correlation premium and show that the consideration of stochastic correlation is a key element for the valuation of these structures.

PRICING TWO-ASSET BARRIER OPTIONS UNDER STOCHASTIC CORRELATION VIA PERTURBATION

2015 ◽  
Vol 18 (03) ◽  
pp. 1550018 ◽  
Author(s):  
MARCOS ESCOBAR ◽  
BARBARA GÖTZ ◽  
DANIELA NEYKOVA ◽  
RUDI ZAGST
Keyword(s):  
Perturbation Theory ◽  
Stochastic Volatility ◽  
Correlation Structure ◽  
Barrier Options ◽  
Correlation Effects ◽  
Stochastic Correlation ◽  
Black Scholes ◽  
Leading Term ◽  
Path Dependent ◽  
Correction Terms

The correlation structure is crucial when pricing multi-asset products, in particular barrier options. In this work, we price two-asset path-dependent derivatives by means of perturbation theory in the context of a bi-dimensional asset model with stochastic correlation and volatilities. To our best knowledge, this is the first attempt at pricing barriers with stochastic correlation. It turns out that the leading term of the approximation corresponds to a constant covariance Black–Scholes type price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function

2014 ◽  
Vol 18 (3) ◽  
Author(s):  
José Da Fonseca ◽  
Martino Grasselli ◽  
Florian Ielpo
Keyword(s):  
Characteristic Function ◽  
Financial Markets ◽  
Empirical Characteristic Function ◽  
Correlation Effects ◽  
Correlation Model ◽  
Moment Conditions ◽  
Gmm Estimation ◽  
Estimation Strategy ◽  
Stochastic Correlation ◽  
Asymmetric Correlation

AbstractThis paper provides the first estimation strategy for the Wishart Affine Stochastic Correlation (WASC) model. We provide elements showing that the use of empirical characteristic function-based estimates is advisable as this function is exponential affine in the WASC case. We use a GMM estimation strategy with a continuum of moment conditions based on the characteristic function. We present the estimation results obtained using a dataset of equity indexes. The WASC model captures most of the known stylized facts associated with financial markets, including leverage and asymmetric correlation effects.

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