Add training workflow, datasets, and runbook

training_data/curated/text/c2b070ee76a27fb475409909e2da07ff8eba861b8a5aa25fc55d50d92a78de6c.txt

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+Chapter 28: Mathematical Applications 
+Theoretical option price= pN(d 1) se-rtN(d2) 
+p v2 
+ln(8 )+ (r +2 )t 
+where d1 = _ r. 
+V-4 t 
+d2 = d1 - v--ft 
+The variables are: 
+p = stock price 
+s = striking price 
+t = time remaining until expiration, expressed as a percent of a year 
+r = current risk-free interest rate 
+v = volatility measured by annual standard deviation 
+ln = natural logarithm 
+N(x) = cumulative normal density function 
+457 
+An important by-product of the model is the exact calculation of the delta - that 
+is, the amount by which the option price can be expected to change for a small 
+change in the stock price. The delta was described in Chapter 3 on call buying, and 
+is more formally known as the hedge ratio. 
+Delta= N(d1) 
+The formula is so simple to use that it can fit quite easily on most programmable cal­
+culators. In fact, some of these calculators can be observed on the exchange floors as 
+the more theoretical floor traders attempt to monitor the present value of option pre­
+miums. Of course, a computer can handle the calculations easily and with great 
+speed. A large number of Black-Scholes computations can be performed in a very 
+short period of time. 
+The cumulative normal distribution function can be found in tabular form in 
+most statistical books. However, for computation purposes, it would be wasteful to 
+repeatedly look up values in a table. Since the normal curve is a smooth curve (it is 
+the "bell-shaped" curve used most commonly to describe population distributions), 
+the cumulative distribution can be approximated by a formula: 
+x = l-z(l.330274y 5 - l.821256y 4 + l.781478y 3 - .356538y 2 + .3193815y) 
+where y 1 and z = .3989423e-<r212 
+= 1 + .2316419lcrl 
+Then N(cr) = x if cr > 0 or N(cr) = 1- x if cr < 0