Black Scholes: Option Pricing

I thank God for blogging. It forces me to put my thoughts into words, helping me to think clearly.

Inputs:

• Share Price (S) in dollars
• Exercise Price (K) in dollars
• Dividend yield (q) in percent (continuously paying)
• Risk-free rate (r ) in percent and p.a.
• Volatility ( vol ) in percent
• Time of maturity (T) in years or Option Life (T-t) (it doesnt matter

Output:

• European Call and Put Option

Method: Black-Scholes Merton

• With or without dividends, we can use the same formula.
• d1 = Ln(So / K) + (r - q + vol ^ 2 / 2) * T / (vol * Sqr(T)
• d2 = Ln(So / K) + (r - q - vol ^ 2 / 2) * T / (vol * Sqr(T))
• z  * (So * Exp(-q * T) * nd1 - K * Exp(-r * T) * nd2)
• if z = 1, we have a call option 
• if z = -1, we have a put option
• nd1 and nd2 are standard normal distribution of d1 and d2 respectively.

Sources:

• http://www.global-derivatives.com/index.php/component/content/52?task=view
• Black, F. & Scholes, M. "The Pricing of Options & Corporate Liabilities" The Journal of Political Economy (May '73)
• Hull, J. "Options, Futures & Other Derivatives" 5th Edition 2002 - Chapter 12