Financial Derivatives: The New Gold?

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 ...

New Results on Deterministic Pricing of Financial Derivatives

Monte Carlo simulation is widely used to price complex nancial instruments. Recent theoretical results and extensive computer testing indicate that deterministic methods may be far superior in speed and conndence. Simulations using the Sobol or Faure points are examples of deterministic methods. For the sake of brevity, we refer to a deterministic method using the name of the sequence of points...

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