OM Session 1 : Introduction to Black & Scholes


The Options Mechanics Group shall meet again on Aug 8th (i.e. every second week).
We shall review the Black & Scholes model and particularly Greeks again in more detail. Rest assured that we'll soon only consider the main B&S equations as generic formulae such as Option Price = Function(Underlying, Option Strike, Implied Volatility, Time To Maturity, Risk-Free Rate, Dividend Yield), i.e. a function of 6 variables.
The objective of the first set of presentations is to be able to understand how to build a Option Pricer.

In the future, I shall leave more advanced content to a blog entry here on this forum.

Attached: Powerpoint presentation and a short doc that summarises B&S.
Links: B&S on Wikipedia, B&S Greeks on Wikipedia


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BSM practitioner observations with respect to index options such as SPX (IMHO)
1) The BSM assumptions which introduce noticeable error are the two relating to volatility (See Bruno's BlackScholes.docx 1st paragraph), 1st assumption of constant volatility, and 2nd the result of historical prices of the underlying.
2) By using implied volatility of the option instead of the underlying historical volatility, these assumptions are no longer error sources. (Equation is calibrated for each use)


Thanks Gary, for pointing that out. I think it is clear in everybody's mind that volatility is not constant.
In future sessions I might forewarn that the topic will be advanced or not, and one of them (I very briefly touched on last time) is the assumption of lognormal price distribution that is one premise of the Geometric Brownian Motion (GBM), B&S is 100% based on.
There has been a lot of research and improvements on B&S since the early 90s with regard to B&S and its interpretation of non-constant volatility across the option chain (local, stochastic, etc).