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Derivatives Week Page 1 of 4 file://C:\WINNT\Profiles\Administrator\Desktop\DW2000.htm 11/16/00
 

Summary: Derivatives Week Page 1 of 4
file://C:\WINNT\Profiles\Administrator\Desktop\DW2000.htm 11/16/00
November 13, 2000 VOL. IX, NO. 46
VARIANCE SWAP VOLATILITY AND OPTION STRATEGIES
Published on 10/30/00.
Born in the over-the-counter derivatives market, variance swap volatility (VSV) is
slowly but surely gaining recognition as a useful tool for managing option positions.
Let's begin with this concept by looking at a variance swap contract.
Here's how it works: Counterparty A agrees to pay Counterparty B a fixed notional
amount due at the settlement date. In exchange, Counterparty B will pay Counterparty
A an amount proportional to the sum of the daily squared returns
where n= number of business days until settlement, and Si,i=0,2,...,n represent daily
closing prices of the underlying stock or index. The sum of the daily returns squared
can be interpreted as an estimator of the realized variance of stock returns from now to
the settlement of the contract.
For instance, a contract can be stipulated as follows: using the Standard & Poor's
500 as the underlying index, a volatility level of * =23% is fixed for one year. This
corresponds to a nominal variance =5.29%. Counterparty B agrees to pay A
USD100,000 for each percentage point of realized variance above *2
=5.29% (where

  

Source: Avellaneda, Marco - Department of Mathematics, Courant Institute of Mathematical Sciences, New York University

 

Collections: Mathematics