In this paper we propose a diffusion model relating the stock price dynamics to the CDS spread dynamics of a company by assuming a linear relationship between instantaneous stock volatility and CDS spread. To value contingent claims under this model we apply a finite elements discretization to...

In this paper we construct arbitrage-free call price surfaces from observed market data by locally constrained least squares approximations. The algorithm computes derivatives of the call surface accurately so that implied volatility, local volatility and transition probability density can be...

In recent years non-linear Black-Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black-Scholes concept. In this article we discuss the applicability of implicit numerical schemes for the valuation of contingent claims in...