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This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained...
Persistent link: https://www.econbiz.de/10005083672
In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to...
Persistent link: https://www.econbiz.de/10009372127
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second...
Persistent link: https://www.econbiz.de/10010599896
We consider $N$ Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion $L_N$ of variables in a given state converge at rate 1/N as $N\rightarrow \infty$. Based...
Persistent link: https://www.econbiz.de/10010600008
This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the...
Persistent link: https://www.econbiz.de/10008611524
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based)...
Persistent link: https://www.econbiz.de/10008611530
In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [Forsyth & Labahn, 2007], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American...
Persistent link: https://www.econbiz.de/10008765887
We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a...
Persistent link: https://www.econbiz.de/10008876617
We extend existing models in the financial literature by introducing a cluster-derived canonical vine (CDCV) copula model for capturing high dimensional dependence between financial time series. This model utilises a simplified market-sector vine copula framework similar to those introduced by...
Persistent link: https://www.econbiz.de/10011067182
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion...
Persistent link: https://www.econbiz.de/10011082821