## Derivations and calculations related to the Black-Scholes Formalism

The Black-Scholes model for financial derivatives has had an extraordinary effect on the financial world. It spawned new areas of business and as of 2016, the approximate notional value of derivative financial instruments valued by Black-Scholes and successor models was $500 trillion dollars.

This result also led to the Nobel Prize for Myron Scholes and Robert Merton in 1997 (Fisher Black died in 1995). https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model

The model has a representation in terms of a partial differential equation as well as the famous Black-Scholes formula for the fair value of options with European style exercise. Understanding this theoretical/mathematical framework for modeling options and other contingent claims is a fundamental requirement for those who work with financial derivatives and I spent much time on it during my years as a quant. I share some Mathematica notebooks related to various aspects of the Black-Scholes-Merton modeling formalism.

**17-1 Derivation of classic Black-Scholes partial differential equation**

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**17-2 Black-Scholes partial differential equation when a foreign currency is involved**

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**17-3 Black-Scholes partial differential equation for two stocks**

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**17-9 Derivation of Black-Scholes formula by calculating an expectation**

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**17-10 Solving BS PDE for call option 01-10-11**

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