The magic number pi is used almost everywhere.

To calculate the Vega in a Black-Scholes world you need to calculate the normal density function. To calculate the normal density function you need the magic number pi. To get a more accurate Vega value you just need to increase the accuracy of pi. Below is the Vega formula for a Black-Scholes stock option with pi in 1000 digits:


To increase the accuracy of Vega further you can just add billions of more known digits and a infinite number of unknown digits to the magic pi.

"Exploring pi is like exploring the universe."

David Chudnovsky


"If you understand Vega in every detail you almost understand the universe "

Espen G. Haug

By the way, Vega is the name of a star and not a Greek like the other option sensitivities.


"The girl my brother knew found out exactly what pi equals,

but she went nuts"

From The Joy of PI book by David Blatner

I can strongly recommend this book to anybody involved in option trading.


copyright Espen Haug 1998- 2004 all rights reserved