Stochastic grid bundling method for backward stochastic differential equations

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations. The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving backward stochastic

An SGBM-XVA demonstrator: A scalable Python tool for pricing XVA

In this work, we developed a Python demonstrator for pricing total valuation adjustment (XVA) based on the stochastic grid bundling method (SGBM). XVA is an advanced risk management concept which became relevant after the recent financial crisis. This work is a follow-up work on Chau and Oosterlee in (Int J Comput Math 96(11):2272–2301, 2019), in which we extended SGBM to numerically solving backward stochastic differential equations (BSDEs). The motivation for this work is basically two-fold. On the application side, by focusing on a particular financial application of BSDEs, we can show the potential of using SGBM on a real-world risk management problem. On the implementation side, we explore the potential of developing a simple yet highly efficient code with SGBM by incorporating CUDA Python into our program

Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results

Rule-based strategies for dynamic life cycle investment

In this work, we consider rule-based investment strategies for managing a defined contribution pension savings scheme, under the Dutch pension fund testing model. We find that dynamic, rule-based investment strategies can outperform traditional static strategies, by which we mean that the investor may achieve the target retirement income with a higher probability or limit the shortfall when the target is not met. In comparison with dynamic programming-based strategies, the rule-based strategies have more stable asset allocations throughout time and avoid excessive transactions that may be hard to explain to an investor. We also study a combined strategy of a rule-based target with dynamic programming. A key feature of our setting is that there is no risk-free asset, instead, a matching portfolio is introduced for the investor to avoid unnecessary risk

SGBM-XVA

This project is a Python demonstrator for the stochastic grid bundling method (SGBM) to solve backward stochastic differential equations (BSDE) (see https://arxiv.org/abs/1801.05180), using the particular case of XVA calculation with Black-Scholes model. It makes use of parallel computing with the CUDA Python platform (https://developer.nvidia.com/how-to-cuda-python) to increase the efficiency of the algorithm. While the functions in this project are tailored to the specific problem of XVA, it can be adapted to general Lipschitz BSDEs with proper modification

On the wavelet-based SWIFT method for backward stochastic differential equations

We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation. We test our algorithm with different numerical experiments

An ab initio study on SnCl2 and Franck-Condon factor simulations of its a-X and B-X absorption and single-vibronic level emission spectra

Minimum-energy geometries, harmonic vibrational frequencies, and relative electronic energies of some low-lying singlet and triplet electronic states of stannous dichloride, SnCl2, have been computed employing the complete-active-space self-consistent-field/multireference configuration interaction (CASSCF/MRCI) and/or restricted-spin coupled-cluster single-double plus perturbative triple excitations [RCCSD(T)] methods. The small core relativistic effective core potential, ECP28MDF, was used for Sn in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. Effects of outer core electron correlation on computed geometrical parameters have been investigated, and contributions of off-diagonal spin-orbit interaction to relative electronic energies have been calculated. In addition, RCCSD(T) or CASSCF/MRCI potential energy functions of the 1A1, ã 3B1, and 1B1 states of SnCl2 have been computed and used to calculate anharmonic vibrational wave functions of these three electronic states. Franck-Condon factors between the 1A1 state, and the ã 3B1 and 1B1 states of SnCl2, which include anharmonicity and Duschinsky rotation, were then computed, and used to simulate the ã- and - absorption and corresponding single-vibronic-level emission spectra of SnCl2 which are yet to be recorded. It is anticipated that these simulated spectra will assist spectroscopic identification of gaseous SnCl2 in the laboratory and/or will be valuable in in situ monitoring of SnCl2 in the chemical vapor deposition of SnO2 thin films in the semiconductor gas sensor industry by laser induced fluorescence and/or ultraviolet absorption spectroscopy, when a chloride-containing tin compound, such as tin dichloride or dimethyldichlorotin, is used as the tin precursor

An ab initio study on some low-lying singlet and triplet states of SbO2+ and quartet states of SbO2

RCCSD(T) calculations on low-lying singlet and triplet states of SbO2+, employing basis sets of up to aug-cc-pV5Z quality, give a linear state with computed adiabatic and vertical ionization energies of 10.11 and 10.65 eV, respectively. CASSCF/MRCI calculations on low-lying quartet states of SbO2 give the lowest quartet state, an (a) over tilde (4)A(1) state, with a T-e of 53.7 kcal mol(-1) (2.33 eV). Reliable ionization energies to the (a) over tilde B-3(2) and (b) over tilde (3)A(2) states of SbO2+ and vertical excitation energies from the (X) over tilde (2)A(1) state of SbO2 to low-lying doublet and quartet states have also been computed to assist future spectroscopic identification of SbO2