Black-Scholes formula

The best modeling framework for R D options is, however, more contentious. The famous, or infamous, Black-Scholes formula [8], based on valuation of traded hnancial options, has in our view impeded the practical use of decision analysis methods by scientihc managers ... 

The price behavior of financial instruments. One of the key assumptions of option pricing models such as Black-Scholes (B-S), which is discussed below, is that asset prices follow a lognormal distribution— that is, the logarithms of the prices show a normal distribution. This characterization is not strictly accurate prices are not lognormally distributed. Asset returns, however, are. Returns are defined by formula (8.8). 

The figure on the following page shows the spreadsheet formulas required to build the Black-Scholes model in Microsoft Excel. The Analysis Tool-Pak add-in must be available, otherwise some of the function references may not work. Setting up the cells in the way shown enables the fair value of a vanilla call or put option to be calculated. The latter calculation employs the put-call parity theorem. 

Thus, we end up with the well known Black and Scholes -like formula for the price of a European call option on a zero-coupon bond... 

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