Derivative instruments

The background and mathematics to martingales can be found in Harrison and Kreps (1979) and Harrison and Pliska (1981) as well as Baxter and Rennie (1996). For a description of how, given that price processes are martingales, we are able to price derivative instruments, see James and Webber (2000, Chapter 3). 

Inflation-linked derivative instruments are now widely traded in the capital markets divisions of investment banks that trade the sovereign inflation-linked bonds. Many smaller banks with regional dominance are also building up their trading capabilities as they rise to meet the increasing demand from their client base for inflation-linked products. 

Although the products typically identify with structured credit seem extensive and often confusing, reflecting the numerous underlyings that are possible bonds, loans, credit default swaps, and so on versus CBOs, CLOs, CSOs, and so on. They all achieve a very similar value proposition they are vehicles to pool and redistribute risk. In many ways, all these products are best classified as derivative instruments given that they... 

Consequently, interest rate swaps can be viewed as a package of more basic interest rate derivative instruments—forwards. The pricing of an interest rate swap will then depend on the price of a package of forward contracts with the same settlement dates in which the underlying for the forward contract is the same reference rate. 

The legal department of most firms that buy or sell credit derivative instruments carefully monitor the terms of the transaction and in particular will focus on any nonstandard terms. In most cases the market will trade on standard ISDA documentation (terms and definitions). Sources of dispute, which are rare, may arise on the actual contract terms the nature of credit events, the obligation selected by the protection buyer for delivery. 

A total return swap (TRS) is a derivative instrument that allows the protection buyer to swap the total economic return of an asset (e.g., loans or securities) for fixed or floating interest payments. 

The following terminology may be nsed to describe the credit risk in bond positions ( cash instruments ) and credit defanlt swaps positions ( credit derivative instruments ) ... 

An investor should be able to replicate the index and its performance with a small number of instruments as well as with relatively low transaction costs and without moving the market too much. For this reason the index constituents should be a set of bonds that have standard features, are liquid, and trade actively in the secondary market. The ability to invest in the index through derivative instruments such as futures and total return swaps is an added attraction of an index. 

Credit-linked notes (CLNs) are the simplest of all credit derivative instruments. They are funded assets issued by a bank or other entity and have credit risk to a second issuer (the Reference Issuer). These notes pay an enhanced coupon to the investor for taking on the added credit risk. These are typically issued our of repackaging vehicles or EMTN programmes. 

Which factors the model incorporates depends in part on the purpose it is intended to serve—whether, for example, it is being used for pricing or hedging derivative instruments or for arbitrage trading. Other considerations also apply, such as the ease and readiness with which the parameters involved can be determined. 

Equation (4.21) states that the dynamics of the forward-rate process, beginning with the initial rate/(0, J), are specified by the set of Brownian motion processes and the drift parameter. For practical applications, the evolution of the forward-rate term structure is usually derived in a binomial-type path-dependent process. Path-independent processes, however, have also been used, as has simulation modeling based on Monte Carlo techniques (see Jarrow (1996)). The HJM approach has become popular in the market, both for yield-curve modeling and for pricing derivative instruments, because it matches yield-curve maturities to different volatility levels realistically and is reasonably tractable when applied using the binomial-tree approach. 

This part also considers the primary fixed-income derivative instruments. These are not securities in the cash markets and are fixed-income derivatives (or interest rate derivatives) in the synthetic markets. 

Pricing Derivative Instruments Using the Black-Scholes Model... 

---