Numerical experiments, Tips, Tricks and Gotchas

Numerically speaking

Black-Scholes equation



The derivation of the Black-Scholes equation is described elsewere (see e.g. the links below). Here I implemented the solution for option pricing as a Windows program.


Assumptions (summary):

 * The price of the underlying instrument St follows a geometric Brownian motion with constant drift μ and volatility σ:

* It is possible to short sell the underlying stock.
* There are no arbitrage opportunities.
* Trading in the stock is continuous.
* There are no transaction costs or taxes.
* All securities are perfectly divisible.
* It is possible to borrow and lend cash at a constant risk-free interest rate r.




Prices, Greeks

The plots of prices


and the Greeks (Delta, Gamma, Vega, Theta, Rho) as functions of a stock price are available for the Call and Put European options:



Here I reproduced well-known results (see e.g. [1]) using my libraries. Feel free to download and play (at your own risk ).

I am adding several new features, please check later.



Black-Scholes pricing program (zipped exe).

Source code (Delphi 7 and up).


References / Links

  1. BlackScholes (From Wikipedia, the free encyclopedia) http://en.wikipedia.org/wiki/Black-Scholes
  2. Greeks, by Liuren Wu http://faculty.baruch.cuny.edu/lwu/9797/Lec7.pdf
  3. Discrete Artificial Boundary Conditions for the Black-Scholes... http://finance.wharton.upenn.edu/~benninga/mma/MiER64.pdf
  4. Binomial Option Pricing, the Black-Scholes Option Pricing Formula http://finance.wharton.upenn.edu/~benninga/mma/MiER64.pdf


© Nikolai Shokhirev, 2012-2017

email: nikolai(dot)shokhirev(at)gmail(dot)com