An equivalent sigma-martingale measure (EsigmaMM) for a given stochastic process S is a probability measure R equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an EsigmaMM is equivalent to a classical absence-of-arbitrage property of S, and is invariant if...

The first three factors resulting from a principal components analysis of term structure data are in the literature typically interpreted as driving the level, slope and curvature of the term structure. Using slight generalisations of theorems from total positivity, we present sufficient...

This paper gives an overview of results and developments in the area of pricing and hedging contingent claims in an incomplete market by means of a quadratic criterion. We first present the approach of risk-minimization in the case where the underlying discounted price process X is a local...

A P-sigma-martingale density for a given stochastic process S is a local P-martingale Z0 starting at 1 such that the product ZS is a P-sigma-martingale. Existence of a P-sigma-martingale density is equivalent to a classic absence-of-arbitrage property of S, and it is invariant if we replace the...

In a numéraire-independent framework, we study a financial market with N assets which are all treated in a symmetric way. We define the fundamental value *S of an asset S as its superreplication price and say that the market has a strong bubble if *S and S deviate from each other. None of these...

Macaulay duration approximates the yield elasticity of bond price. Since its introduction in 1938 researchers have sought a more accurate formula. This article demonstrates Macaulay's formula gives accurate results if applied appropriately. A bond with maturity n has n solutions for yield, one...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...

In the banking industry, the common practice to correlate default and migration events of various guarantors is to use correlated asset price returns. This approach, which is basically a copula approach, is used also by KMV's GCorr model and JPMorgan's CreditMetrics model. However, these models...

Introducing the Brownian motion in the way of Einstein and Wiener we find the connection between a Wiener Process and the Heat Diffusion PDE.We solve the PDE analytically for some boundary conditions and then use the connection to the Wiener Process to solve more complex BVP's using Monte Carlo...