Chapter 7: Brief Technical Background. BLACK-SCHOLES MODEL. The cumulative standard-normal distribution function can be solved in Excel by using its “NORMSDIST( )” function. | Two Technical Background of the Binomial Lattice and Black-Scholes Models NKI7 Brief Technical Background BLACK-SCHOLES MODEL The basic BSM is summarized as follows Call S ln S X rf g2 2T - Xe -rf T ln S X rf - g2 2T gT vJt Put Xe - rf T ln S X rf - g2 2T - S - ln S X rf g2 2T gT gT where 0 is the cumulative standard-normal distribution function S is the value of the forecast stock price at grant date X is the option s contractual strike price rf is the nominal risk-free rate o is the annualized volatility T is the time to expiration of the option To illustrate its use let us assume that an option exists such that both the stock price S and the strike price X are 100 the time to expiration T is one year with a 5 percent annualized risk-free rate rf for the same duration while the annualized volatility o of the underlying asset is 25 percent. The BSM calculation yields .
