Path Integrals and Hamiltonians for Options and Interest Rates
By Belal E. Baaquie
Publisher: Cambridge University Press
Print Publication Year: 2004
Online Publication Date:February 2010
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511617577.005
Derivative securities, or derivatives in short, are important forms of financial instruments that are traded in the financial markets. As the name implies, derivatives are derived from underlying financial instruments: the cash flows of a derivative depend on the prices of the underlying instruments.
Derivatives have many uses from being an ingredient in the hedging of a portfolio, to their use as instruments for speculation.
Given the uncertainties of the financial markets, there is a strong demand from the market for predicting the future behaviour of securities. Derivative instruments are a response to this need, and contain information for estimating the behaviour of a security in the future. There are three general categories of derivatives, namely forwards, futures and options.
Forward and futures contracts
Suppose a corporation needs to import steel one year in the future, denoted by T. Since the price of steel can vary over time, the corporation would like to guard against the risk of the price of steel increasing by locking-in the price of steel today, denoted by t.
Let the price of steel per ton at time t be denoted by S(t). The forward contract is a contract between a buyer of steel – who is said to have a long position, and a seller – who is said to have a short position. The seller agrees, at time t, to provide steel at future time T, at the forward price F(t, T) that reflects the current prevailing price and interest rates.