BENCHOP–SLV: the BENCHmarking project in Option Pricing–Stochastic and Local Volatility problems

In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE) formulation and the Partial Differential Equation (PDE) formulation of the problem, as well as Fourier methods making use of the characteristic function, were implemented to solve these problems. Comparisons are made with respect to time to reach a certain error level in the computed solution for the different methods. The implemented Fourier method was superior to all others for the two problems where it was implemented. Generally, methods targeting the PDE formulation of the problem outperformed the methods for the SDE formulation. Among the methods for the PDE formulation the ADI method stood out as the best performing one

ADI finite difference schemes for the Heston-Hull-White PDE

In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider the Heston-Hull-White model with arbitrary correlation factors, with time-dependent mean-reversion levels, with short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. In addition, both European-style call options and up-and-out call options are considered. It is shown through extensive tests that ADI schemes, with a proper choice of their parameters, perform very well in all situations - in terms of stability, accuracy and efficiency.

Selection of the model explaining variations of the group’s fission probability.

<p>We represented the variables included in the 12 best models that have ΔAIC≤2, with their respective AIC values, ΔAIC, their AIC weights (AIC_w) and the cumulative sum of the AIC weights (acc AIC_w). We also present the cumulative sum of the AIC_w in which each variable is presented, giving the variable’s AIC weight (w_i; in line).</p>1<p>interaction: <i>Male:Period:DomAct</i>.</p>2<p>interaction: <i>Male:Period:Gpsize</i>.</p