Risk Management and Financial Institutions, + Web Site, 3rd Edition

APPENDIX E

Valuing European Options

The Black–Scholes–Merton formulas for valuing European call and put options on an investment asset that provides no income are

and

where

The function N(x) is the cumulative probability distribution function for a standardized normal distribution (see tables at the end of the book or Excel’s NORMSDIST function). The variables c and p are the European call and European put price, S0 is today’s asset price, K is the strike price, r is the continuously compounded risk-free rate, σ is the stock price volatility, and T is the time to maturity of the option.

When the underlying asset provides a cash income, the present value of the income during the life of the option should be subtracted from S0. When the underlying asset provides a yield at rate q, the formulas become

and

where

Options on a foreign currency can be valued by setting q equal to the foreign ...