In this paper analytical solutions for European option prices are derived for a class of rather general asset specific pricing kernels (ASPKs) and distributions of the underlying asset. Special cases include underlying assets that are lognormally or log-gamma distributed at expiration date T....

In this paper analytical solutions for European option prices are derived for a class of rather general asset specific pricing kernels (ASPKs) and distributions of the underlying asset. Special cases include underlying assets that are lognormally or log-gamma distributed at expiration date T....

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In particular, the compact schemes of Rigal are generalized. The numerical results are compared to standard...

Based on a general specification of the asset specific pricing kernel, we develop a pricing model using an information process with stochastic volatility. We derive analytical asset and option pricing formulas. The asset prices in this rational expectations model exhibit crash-like, strong...

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a...

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the...

Recent research suggests that the power law is one of the most universal laws in nature and it also seems to work quite fine in economics and finance. In this paper we show that the power law explains extremely well the relationship between the value of broad-based market indices and their...