# American Institute of Mathematical Sciences

October  2015, 11(4): 1185-1209. doi: 10.3934/jimo.2015.11.1185

## A closed-form solution for outperformance options with stochastic correlation and stochastic volatility

 1 BBVA and University Institute for Economic and Social Analysis, University of Alcalá, Mailing address: c/ Sauceda, 28 Edicio ASIA, 28050, Madrid, Spain

Received  January 2014 Revised  September 2014 Published  March 2015

Outperformance options allow investors to benefit from a view on the relative performance of two underlying assets without taking any directional exposure to the evolution of the market. These structures exhibit high sensitivity to the correlation between the underlying assets and are usually priced assuming constant instantaneous correlations.
This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the assets returns, as well as between their volatilities. Under the assumptions of the model this article provides semi-closed form solutions for the price of outperformance options. The article shows that the price of these options depends crucially on the term structure of the correlation corresponding to the assets returns. Furthermore, the comparison of the prices obtained under this model and under other models with constant correlations commonly used by financial institutions reveals the existence of a stochastic correlation premium.
Citation: Jacinto Marabel Romo. A closed-form solution for outperformance options with stochastic correlation and stochastic volatility. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1185-1209. doi: 10.3934/jimo.2015.11.1185
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##### References:
 [1] Jia Yue, Nan-Jing Huang. Neutral and indifference pricing with stochastic correlation and volatility. Journal of Industrial & Management Optimization, 2018, 14 (1) : 199-229. doi: 10.3934/jimo.2017043 [2] Christoforidou Amalia, Christian-Oliver Ewald. A lattice method for option evaluation with regime-switching asset correlation structure. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020042 [3] Min Niu, Bin Xie. Comparison theorem and correlation for stochastic heat equations driven by Lévy space-time white noises. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 2989-3009. doi: 10.3934/dcdsb.2018296 [4] Lixin Wu, Fan Zhang. LIBOR market model with stochastic volatility. Journal of Industrial & Management Optimization, 2006, 2 (2) : 199-227. doi: 10.3934/jimo.2006.2.199 [5] Lassi Roininen, Markku S. Lehtinen, Sari Lasanen, Mikko Orispää, Markku Markkanen. Correlation priors. Inverse Problems & Imaging, 2011, 5 (1) : 167-184. doi: 10.3934/ipi.2011.5.167 [6] Kais Hamza, Fima C. Klebaner, Olivia Mah. Volatility in options formulae for general stochastic dynamics. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 435-446. doi: 10.3934/dcdsb.2014.19.435 [7] Harish Garg. Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1501-1519. doi: 10.3934/jimo.2018018 [8] Ming Su, Arne Winterhof. Hamming correlation of higher order. Advances in Mathematics of Communications, 2018, 12 (3) : 505-513. doi: 10.3934/amc.2018029 [9] Vladimír Špitalský. Local correlation entropy. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5711-5733. doi: 10.3934/dcds.2018249 [10] Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279 [11] Martino Bardi, Annalisa Cesaroni, Daria Ghilli. Large deviations for some fast stochastic volatility models by viscosity methods. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3965-3988. doi: 10.3934/dcds.2015.35.3965 [12] Laurent Devineau, Pierre-Edouard Arrouy, Paul Bonnefoy, Alexandre Boumezoued. Fast calibration of the Libor market model with stochastic volatility and displaced diffusion. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1699-1729. doi: 10.3934/jimo.2019025 [13] Nian Li, Xiaohu Tang, Tor Helleseth. A class of quaternary sequences with low correlation. Advances in Mathematics of Communications, 2015, 9 (2) : 199-210. doi: 10.3934/amc.2015.9.199 [14] Xin-Guo Liu, Kun Wang. A multigrid method for the maximal correlation problem. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 785-796. doi: 10.3934/naco.2012.2.785 [15] Kaitlyn (Voccola) Muller. SAR correlation imaging and anisotropic scattering. Inverse Problems & Imaging, 2018, 12 (3) : 697-731. doi: 10.3934/ipi.2018030 [16] Lorella Fatone, Francesca Mariani, Maria Cristina Recchioni, Francesco Zirilli. Pricing realized variance options using integrated stochastic variance options in the Heston stochastic volatility model. Conference Publications, 2007, 2007 (Special) : 354-363. doi: 10.3934/proc.2007.2007.354 [17] Yan Zhang, Yonghong Wu, Benchawan Wiwatanapataphee, Francisca Angkola. Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework. Journal of Industrial & Management Optimization, 2020, 16 (1) : 71-101. doi: 10.3934/jimo.2018141 [18] Yu Zheng, Li Peng, Teturo Kamae. Characterization of noncorrelated pattern sequences and correlation dimensions. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5085-5103. doi: 10.3934/dcds.2018223 [19] Houduo Qi, ZHonghang Xia, Guangming Xing. An application of the nearest correlation matrix on web document classification. Journal of Industrial & Management Optimization, 2007, 3 (4) : 701-713. doi: 10.3934/jimo.2007.3.701 [20] Jana Majerová. Correlation integral and determinism for a family of $2^\infty$ maps. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5067-5096. doi: 10.3934/dcds.2016020

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