Numerical experiments, Tips, Tricks and Gotchas
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.
* The price of the underlying instrument S_{t} 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.
Info |
Prices, Greeks |
The plots of prices
Prices |
and the Greeks (Delta, Gamma, Vega, Theta, Rho) as functions of a stock price are available for the Call and Put European options:
Deltas |
Gamma |
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).
© Nikolai Shokhirev, 2012-2017
email: nikolai(dot)shokhirev(at)gmail(dot)com