A Brief History of Derivatives - Don Chance

Submitted by cahn on 30 January, 2010 - 1:21pm
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 To start we need to go back to the Bible. In Genesis Chapter 29, believed to be about the year 1700 B.C., Jacob purchased an option costing him seven years of labor that granted him the right to marry Laban's daughter Rachel. His prospective father-in-law, however, reneged, perhaps making this not only the first derivative but the first default on a derivative.

Variance Notional vs. Vega Notional

Submitted by cahn on 30 September, 2009 - 2:21pm

In Variance Swap, the relationship between  Vega Notional (the dollar value per vega or volatility point) and Variance Notional (the dollar value per variance unit) is conventionally expressed as

\[VarianceNotional=\frac{VegaNotional}{2K_{Var}}\]

The $ 2K_{Var} $ comes from the first order Taylor expansion (expand the function $ f\left(\sigma_{Var}\right)=\sigma_{Var}^2-K_{Var}^2 $).

Stocks and Bonds over Time

Submitted by cahn on 26 September, 2009 - 6:06pm
Stocks and Bonds over Time

Despite a steady rise over most of the past century, the markets have seen plenty of turbulence.

Historical High-Low Volatility: Parkinson

Submitted by cahn on 20 September, 2009 - 1:20am
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The  Parkinson formula for estimating the historical volatility of an underlying based on high and low prices.

$ \sigma = \sqrt{\frac{Z}{n 4 \ln 2}\sum_{i=1}^{n}\left(\ln \frac{H_i}{L_i}\right)^2} $

where

$ \sigma $ = Volatility
$ Z $ = Number of closing prices in a year
$ n $ = Number of historical prices used in the volatility estimate
$ H_i $ = The high
$ L_i $ = The low

http://www.sitmo.com/eq/173

Historical Open-High-Low-Close Volatility: Garman and Klass (Yang Zhang)

Submitted by cahn on 20 September, 2009 - 1:16am
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Yang and Zhang derived an extension to the Garman Glass historical volatility estimator that allows for opening jumps. It assumes Brownian motion with zero drift. This is currently the preferred version of open-high-low-close volatility estimator for zero drift and has an efficiency of 8 times the classic close-to-close estimator. Note that when the drift is nonzero, but instead relative large to the volatility, this estimator will tend to overestimate the volatility.

What did I say then?

Currency controls unlikely to end soon

Submitted by cahn on 27 October, 2008 - 1:13pm
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China is not ready to relax its rigid foreign exchange regime, despite a landmark stock market reform next month that could trigger an influx of overseas cash, economists said yesterday.

The imminent launch of a long-awaited scheme that allows qualified foreign institutional investors (QFII) to buy yuan-denominated A shares has prompted overseas foreign exchange markets to price in a more flexible and stronger yuan.

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