Yield curves are used to imply the forward rates and discount factors from market tradable instruments and are required to discount future cash flows and evaluate the price of all financial contracts. Not all instruments can be included in the yield curve calibration or fitting process, hence we...

In this short paper we outline the Newton-Raphson methods used for solving and minimizing complex equations that often have no analytical solution. We outline the formulae, their origins and give a simple example of their application

Interest rate swaps are an actively traded product in the financial marketplace and are popular for hedging mortgage and corporate loan exposures against rises in interest rates. Asset swaps on the other hand provide a form of asset financing, where investors borrow funds to purchase an asset,...

In this paper we outline the Lagrangian constrained optimization method to solve complex problems subject to constraints. Firstly we summarize the Lagrangian constrained optimization routine. Secondly we outline a detailed implementation strategy. Thirdly and finally we provide example and solve...

In this PowerPoint presentation we give an overview of yield curves, show how they are modelled and calibrated and give a brief overview of LIBOR reform.Firstly we explain how to calibrate curves to imply forward rates & discount factors. Secondly, we outline the interpolation, optimization and...

This study introduces a non linear model of commodity futures prices which accounts for the pressures due to hedging and speculative activities. The interaction with the corresponding spot market is considered assuming that a long term equilibrium relationship holds between futures and spot...

We show how distributions can be reduced to low-dimensional scenario trees. Applied to intertemporal distributions, the scenarios and their probabilities become time-varying factors. From S&P 500 options, two or three time-varying scenarios suffice to forecast returns, implied variance or...

French Abstract: Les Credit Default Swaps (CDS) sont de plus en plus populaires pour la protection contre les défauts et la spéculation. Cette étude se concentre sur la modélisation précise du défaut en temps continu, puis sur l'evaluation des CDS. De nombreux cas entraînent l'annulation...