The Vasicek model (1977) is one of the earliest stochastic models of the term structure of interest rates. This model, though it has it's shortcomings, has many advantages, such as analytical tractability and mean reversion features, and may be viewed as a short rate model template.Several short...

In what follows we outline briefly the Credit Support Annex and how it impacts securities pricing. We then proceed to discuss synthetic forward rate calculation and the FX forward invariance relationship from which we show how to calculate CSA collateral adjusted discount factors using GBP...

Asset swaps provide a form of asset financing, where investors borrow funds to purchase an asset, typically a bond. Asset swaps are also a good bond rich-cheap analysis tool. Such swaps can of course be used for speculative purposes. In this paper we provide a brief overview of asset swaps and...

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...

An option is a financial instrument that allows the holder to buy or sell an underlying security in the future at an agreed strike or price set today. Many options are priced under the assumption of constant interest rates as seen in the Black-Scholes (1973) model. In interest rate markets...

In this paper we review the pricing and model calibration of Credit Default Swaps referring to both the International Swaps and Derivatives Association (ISDA) CDS contract and credit model standardization guidelines. Furthermore we provide an Excel pricing workbook to supplement the materials...

In this article we illustrate how to price bonds and calculate the accrued interest, clean- and dirty price, from which we can compute a bond invoice i.e., the present value for a given cash investment in the bond. We present the classical bond pricing formulae and show how to modify this...

Yield Curves reflect the borrowing and lending rates over a range of maturities within a particular market and currency. Yield curves capture the term structure of interest rates and provide observers with a means of comparing short- and long-term interest rates.There are different types of...

In this paper we outline the European interest rate swaption pricing formula from first principles using the Martingale Representation Theorem and the annuity measure. This leads to an expression that allows us to apply the generalized Black-Scholes result. We show that a swaption pricing...

In this paper we illustrate and explain the relationship between interest rates (or forward rates) and discount factors. We present the forward-discount factor relationship, which is popular and widely used in financial markets for yield curve construction, and derive the exact formulae using a...