Derivative Pricing

New products are notoriously difficult to model and one of the most sensitive factors in such models is the product s proposed price. Consequently qualitative research is most frequently required to derive pricing models for the market and the product. Many times products have been launched with entirely false... 

Thermoeconomic optimization using differentially derived prices, permitting the analysis of the system s local and global responses to well specified small changes in the state of the system, and leading to sensitivity analysis and optimization techniques. 

Baxter, M., Rennie, A., 1996. Financial Calculus. Cambridge University Press, Cambridge. Baxter, M., Rennie, A., 1998. An Introduction to Derivative Pricing. Cambridge University Press, Cambridge (Chapter 5). 

Central banks and market practitioners use interest rates prevailing in the government bond market to extract certain information, the most important of which is implied forward rates. These are an estimate of the market s expectations about the future directirMi of short-term interest rates. They are important because they signify the market s expectafirMis about the future path of interest rates however, they are also used in derivative pricing and to create synthetic bond prices from the extent of credit spreads of corporate bonds. 

In order to examine some of the major developments in option/ derivative pricing in the interest rate field it is appropriate at this point to establish a working framework. 

The reduced form models described earlier models are a new generation of credit derivative pricing models, which are now increasingly being used to price total return swaps. 

Reduced Form Kamakura implements reduced form models from the Robert Jarrow family, such as the Jarrow-Chava version. These models use equity, debt, and credit derivative prices. 

In addition, Kamakura s research has shown that reduced form models utilizing credit derivatives prices are the most effective default predictor ... 

Our results indicate that reduced form models based on credit derivatives prices and bond prices have the best performance from both a statistical and a practical point of view, said Profes-... 

Credit-derivative pricing is similar to the pricing of other off-balance-sheet products, such as equity, currency, and bond derivatives. The main difference is that the latter can be priced and hedged with reference to the underlying asset, and credit derivatives cannot. The pricing model for credit products incorporates statistical data concerning the likelihood of default, the probability of payout, and market level of risk tolerance. 

Once all risk indicators associated with catastrophic events have been identified and properly estimated in terms of frequency of occurrence and impact in the underlying spot price, the respective premium can be calculated under the common assumptions of derivatives pricing. 

Business Portfolio management, derivative pricing, transaction analysis... 

A better measure of the relative value of a bond with an embedded option is the constant spread that, when added to all the short rates in the binomial tree, makes the bond s theoretical (model-derived) price equal to its observed market price. The constant spread that satisfies this requirement is the option-adjusted spread. It is option adjusted because it refiects the option feature attached to the bond. 

We describe first some common inflation derivatives, before considering some uses for hedging and other purposes. We then consider IL derivatives pricing. 

An inflation term structure is a necessary prerequisite to the pricing of inflation derivatives. It is constructed using the same principles we discussed in Chapters 3 and 4. Previously, to construct this curve we would have used IL bond prices as the set of market yields used as inputs to the curve. Now, however, we can also use the prices of IL derivatives. As with other markets, the derivative prices are often preferred to cash prices for two reasons one, we can use a continuous set of prices rather than have to rely on available bond maturities, and two, there is usually greater liquidity in the OTC market. 

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