Section: New Software and Platforms

Algorithms implemented in Premia in 2016

Premia 18 has been delivered to the consortium members in March 2016.

It contains the following new algorithms:

• A Forward Solution for Computing Derivatives Exposure. M. Ben Taarit, B. Lapeyre.

• Monte Carlo Calculation of Exposure Profiles and Greeks for Bermudan and Barrier Options under the Heston Hull-White Model. Q. Feng, C.W. Oosterlee.

• Dynamic optimal execution in a mixed-market-impact Hawkes price model. A. Alfonsi, P. Blanc. Finance & Stochastics

• A Hamilton Jacobi Bellman approach to optimal trade execution. P. Forsyth, Applied Numerical Mathematics 61, 2011.

• Value function approximation or stopping time approximation: a comparison of two recent numerical methods for American option pricing using simulation and regression. L. Stentoft, Journal of Computational Finance, 18( 1), 2014.

• Pricing American-Style Options by Monte Carlo Simulation: Alternatives to Ordinary Least Squares. S. Tompaidis, C. Yang, Journal of Computational Finance, 18(1), 2014,

• Solving Optimal Stopping Problems using Martingale Bases. J.Lelong

• The Stochastic Grid Bundling Method: Efficient Pricing of Bermudan Options and their Greeks. S. Jain, C.W. Oosterlee.

• Two-dimensional Fourier cosine series expansion method for pricing financial options. C.W.Oosterlee M.J. Ruijter, SIAM J. Sci. Comput., 34(5), 2012.

• Estimation of the parameters of the Wishart process. A.Alfonsi, A.Kebaier, C.Rey, Preprint

• The 4/2 Stochastic Volatility Model. M. Grasselli, Preprint.

• Ninomiya Victoir Scheme and Multi Level Scheme. A. Al Gerbi, E. Clement, B. Jourdain.

• Importance Sampling for Multilevel Monte Carlo. A.Kebaier J.Lelong

• The evaluation of barrier option prices under stochastic volatility. C.Chiarella, B.Kang, G.H.Meyer, Computers and Mathematics with Applications 64, 2012.

• Volatility swaps and volatility options on discretely sampled realized variance. G.Lian, C.Chiarella, P.S.Kalev, Journal of Economic Dynamics Control 47 2014

• Efficient variations of the Fourier transform in applications to option pricing. S. Boyarchenko and S.Levendorski, Journal of Computational Finance, 18(2), 2014.

• Model-free implied volatility: from surface to index. M. Fukasawa et al., Int. J. Theor. Appl. Finan. 14, 433, 2011

• Stratified approximations for the pricing of options on average. N.Privault J.Yu Journal of Computational Finance.

Moreover, J. Lelong has ensured everyday maintenance to fix various bugs, especially related to Visual C++; and has get rid of the old bunch of scripts to generate the HTML documentation by implementing the required mechanism directly in TeX. This makes the system much more robust; He has also worked on the continuous integration process with Sébastien Hinderer. Moreover, part of Premia documentation is now generated directly from the source code. The 3000 lines of undocumented C code used so far had become unmaintainable. Now, it is replaced by a much more flexible and efficient Python script.