Numerical schemes and Monte Carlo techniques for Greeks in stochastic volatility models

The main objective of this thesis is to propose approximations to option sensitivities in stochastic volatility models. The first part explores sequential Monte Carlo techniques for approximating the latent state in a Hidden Markov Model. These techniques are applied to the computation of Greeks by adapting the likelihood ratio method. Convergence of the Greek estimates is proved and tracking of option prices is performed in a stochastic volatility model. The second part defines a class of approximate Greek weights and provides high-order approximations and justification for extrapolation techniques. Under certain regularity assumptions on the value function of the problem, Greek approximations are proved for a fully implementable Monte Carlo framework, using weak Taylor discretisation schemes. The variance and bias are studied for the Delta and Gamma, when using such discrete-time approximations. The final part of the thesis introduces a modified explicit Euler scheme for stochastic differential equations with non-Lipschitz continuous drift or diffusion; a strong rate of convergence is proved. The literature on discretisation techniques for stochastic differential equations has been motivational for the development of techniques preserving the explicitness of the algorithm. Stochastic differential equations in the mathematical finance literature, including the Cox-Ingersoll-Ross, the 3/2 and the Ait-Sahalia models can be discretised, with a strong rate of convergence proved, which is a requirement for multilevel Monte Carlo techniques.Open Acces

An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients

We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the optimal strong error rate. We apply this scheme to SDEs widely used in the mathematical finance literature, including the Cox-Ingersoll-Ross~(CIR), the 3/2 and the Ait-Sahalia models, as well as a family of mean-reverting processes with locally smooth coefficients. We numerically illustrate the strong convergence of the scheme and demonstrate its efficiency in a multilevel Monte Carlo setting.Comment: 36 pages, 17 figures, 2 table

Carbon-supported iron complexes as electrocatalysts for the cogeneration of hydroxylamine and electricity in a NO-H-2 fuel cell: A combined electrochemical and density functional theory study

© 2018 Elsevier B.V. Carbon-supported iron complexes were investigated as electrocatalysts for the reduction of nitric oxide (NO) in a H2-NO fuel cell conceived for the production of hydroxylamine (NH2OH) with concomitant generation of electricity. Two types of iron complexes with tetradentate ligands, namely bis(salicylidene)ethylenediimine (Salen) and phthalocyanine (Pc), supported on activated carbon or graphite were prepared and evaluated as electrocatalysts, either without further treatment or after pyrolysis at 700 °C. The performance in the reduction of NO of gas diffusion cathodes based on these electrocatalysts was investigated in an electrochemical half cell (3-electrode configuration) using linear sweep voltammetry (LSV). The most promising electrocatalysts were studied further by chronoamperometric experiments in a H2-NO fuel cell, which allowed comparison in terms of power output and hydroxylamine production. Depending on the concentration of the NO feed (6 or 18%), the best electrocatalytic performance was delivered either by FePc or FeSalen. The gas diffusion electrode based on FeSalen supported on activated carbon with 0.3 wt% Fe-loading provided the highest current density (86 A/m2) and the best current efficiency (43%) towards the desired NH2OH when operating at the higher NO concentration (18%). Moreover, FeSalen offers the advantage of being cheaper than FePc. The experimental work was complemented by density functional theory (DFT) calculations, which allowed to shed more light on the reaction mechanism for the reduction of nitric oxide at the atomistic level.status: publishe

Carbon-supported iron complexes as electrocatalysts for the cogeneration of hydroxylamine and electricity in a NO-H-2 fuel cell: A combined electrochemical and density functional theory study

Carbon-supported iron complexes were investigated as electrocatalysts for the reduction of nitric oxide (NO) in a H-2-NO fuel cell conceived for the production of hydroxylamine (NH2OH) with concomitant generation of electricity. Two types of iron complexes with tetradentate ligands, namely bis(salicylidene)ethylenediimine (Salen) and phthalocyanine (Pc), supported on activated carbon or graphite were prepared and evaluated as electrocatalysts, either without further treatment or after pyrolysis at 700 degrees C. The performance in the reduction of NO of gas diffusion cathodes based on these electrocatalysts was investigated in an electrochemical half cell (3-electrode configuration) using linear sweep voltammetry (LSV). The most promising electrocatalysts were studied further by chronoamperometric experiments in a H-2-NO fuel cell, which allowed comparison in terms of power output and hydroxylamine production. Depending on the concentration of the NO feed (6 or 18%), the best electrocatalytic performance was delivered either by FePc or FeSalen. The gas diffusion electrode based on FeSalen supported on activated carbon with 0.3 wt% Fe-loading provided the highest current density (86 A/m(2)) and the best current efficiency (43%) towards the desired NH2OH when operating at the higher NO concentration (18%). Moreover, FeSalen offers the advantage of being cheaper than FePc. The experimental work was complemented by density functional theory (DFT) calculations, which allowed to shed more light on the reaction mechanism for the reduction of nitric oxide at the atomistic level