In Chapter 3, Using Python as a Financial Calculator, we recommended the combining of many small Python programs as one program. In this chapter, we adopted the same strategy to combine all the programs in a big file p4f.py. For instance, the preceding Python program, that is, the bs_call() function is included. Such a collection of programs offers several benefits. First, when we use the bs_call() function, we don't have to type those five lines. To save space, we will only show a few functions included in p4f.py. For brevity, we will remove all the comments included for each function. Those comments are designed to help future users when issuing the help() function, such as help(bs_call()).

def bs_call(S,X,T,rf,sigma):
    from scipy import log,exp,sqrt,stats
    d1=(log(S/X)+(rf+sigma*sigma/2.)*T)/(sigma*sqrt(T))
    d2 = d1-sigma*sqrt(T)
    return S*stats.norm.cdf(d1)-X*exp(-rf*T)*stats.norm.cdf(d2)

The following program uses a binomial model to price a call...