Financial derivatives use and multifaceted exposures

Financial Derivatives

The Merriam-Webster dictionary defi nes a derivative in the fi eld of chemistry as " a substance that can be made from another substance. " Derivatives in fi nance work on the same principle. These fi nancial instruments promise payoffs that are derived from the value of something else, which is called the " underlying. " The underlying is often a fi nancial asset or rate, but it does not have ...

Pricing of Financial Derivatives

A financial derivative, for example an option, is an instrument (contract) whose value depends on the values of some underlying variables, where the underlying can be a commodity, an interest rate, stock, a stock index, a currency, to mention just a few examples. The financial derivatives market is enormous and is regularly reported to be worth $500 trillion. Derivatives provide an efficient wa...

Analytical approximations for financial derivatives

We propose a new approach to the analytical approximation of transition densities typically arising in finance. This allows to obtain an expansion of the price of financial derivatives using as starting point the classical Black&Scholes formula. Explicit error estimates for the expansion truncated at any order are available. A numerical test is presented and possible applications to Monte Carlo...

Faster Valuation of Financial Derivatives

Pseudorandom Financial Derivatives (working Paper)

Arora, Barak, Brunnermeier, and Ge [ABBG10] showed that taking computational complexity into account, a dishonest seller could increase the lemon costs of a family of financial derivatives dramatically. We show that if the seller is required to construct derivatives of a certain form, then this phenomenon disappears. In particular, we define and construct pseudorandom derivative families, for w...