A heterogeneous computing approach to maximum likelihood parameter estimation for the Heston model of stochastic volatility

Stan Hurn, Kenneth Lindsay, David James Warne

Abstract


Stochastic volatility models are of fundamental importance to the pricing of derivatives. One of the most commonly used models of stochastic volatility is the Heston model in which the price and volatility of an asset evolve as a pair of coupled stochastic differential equations. The computation of asset prices and volatilities involves the simulation of many sample trajectories with conditioning. The problem is treated using the method of particle filtering. While the simulation of a shower of particles is computationally expensive, each particle behaves independently making such simulations ideal for massively parallel heterogeneous computing platforms. We present a portable OpenCL implementation of the Heston model and discuss its performance and efficiency characteristics on a range of architectures including Intel CPUs, Nvidia GPUs, and Intel Many-Integrated-Core accelerators.

References
  • Y. Ait-Sahalia and R. Kimmel. Maximum likelihood estimation of stochastic volatility models. J. Financ. Econ., 83:413–452, 2007. doi:10.1016/j.jfineco.2005.10.006
  • C. S. Forbes, G. M. Martin and J. Wright. Inference for a class of stochastic volatility models using option and spot prices: Application of a bivariate Kalman filter. Economet. Rev., 26:387–418, 2007. doi:10.1080/07474930701220584
  • Khronos Opencl Working Group. The Opencl specification. Technical report, Khronos Group, October 2009. http://www.khronos.org/registry/cl/specs/opencl-1.0.pdf
  • S. L. Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud., 6:326–343, 1993. doi:10.1093/rfs/6.2.327
  • A. S. Hurn, K. A. Lindsay and A. J. McClelland. Estimating parameters of stochastic volatility models using option price data. J. Bus. Econ. Stat., 33(4):579–594, 2015. doi:10.1080/07350015.2014.981634
  • A. S. Hurn, K. A. Lindsay and A. J. McClelland. On the efficacy of Fourier series approximations for pricing European and digital options. Appl. Math., 5(17):2786–2807, 2015. doi:10.4236/am.2014.517267
  • M. S. Johannes, N. G. Polson and J. R. Stroud. Optimal filtering of jump diffusions: Extracting latent states from asset prices. Rev. Financ. Stud., 22:2759–2799, 2009. doi:10.1093/rfs/hhn110
  • V. W. Lee, C. Kim, J. Chhugani, M. Deisher, D. Kim, A. D. Nguyen, N. Satish, M. Smelyanskiy, S. Chennupaty, P. Hammarlund, R. Singhal and P. Dubey. Debunking the 100x GPU vs CPU myth: an evaluation of throughput computing on CPU and GPU. In Proceedings of the 37th Annual International Symposium on Computer Architecture, pages 451–460, New York, NY, USA, 2010. ACM. doi:10.1145/1815961.1816021
  • J. A. Nelder and R. Mead. A simplex method for function minimization. Comput. J., 7(4):308–313, 1965. doi:10.1093/comjnl/7.4.308

Keywords


Stochastic Volatility, Heterogeneous computing, Maximum likelihood, graphics processing unit, many-integrated cores

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DOI: http://dx.doi.org/10.21914/anziamj.v57i0.10425



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