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["       Price of Barrier Options in Binomial Model"]
[]
["Stock Price",10,null,"Enter data in yellow cells"]
["Strike Price",15,null,"or use sample data."]
["Rate per period",1.6438356164383562E-4]
["Periods",15,null,null,"         The program calculates option prices by two methods, deterministic and Monte Carlo. The"]
["u",1.1000000000000001,null,null,"     deterministic method uses an algorithm to generate all possible stock price scenarios in"]
["d",0.7,null,null,"     the form of a sequence of 1's and 0's, 1 representing a 'u'  and 0 zero representing a 'd'."]
["Monte Carlo Sample Size",10000,null,null,"     Sums U_n of these 1's and 0's up through n periods represent binomial random variable values",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5124.4084972941209]
[null,null,null,null,"    and are used to calculate S_n = S_0 * v^Y_n * d^n. The latter values are then used to obtain"]
[null,null,null,null,"    the payoff H. The expectation E*(H) is calculated by multiplying H by the probability of the"]
["Calls","Barriers",null,null,"    scenario and summing over all scenarios. This method is slower and should not be used if the"]
[" Up and out",30,0.9119346910879238,0.91715873700140638,"    number of periods exceeds 18."]
[" Up and in",12,1.4356522434910446,1.4294524150182688,"         The Monte Carlo method uses a random number generator to obtain a stock price scenario."]
[" Down and out",5,1.4328032321793833,1.4271587224195523,"    The payoff H is obtained from the scenario as in the deterministic method. The average of these"]
[" Down and in",9,0.294935438596022,0.30786423916997013,"    payoffs is the sample sum and is taken as an approximation of E*(H) (law of large numbers)."]
[]
["Puts"]
[" Up and out",30,6.3966201698748231,6.4032513760690524]
[" Up and in",12,3.3681949453623421,3.3701953540343439]
[" Down and out",5,2.1375437719462203,2.1366232003658348]
[" Down and in",9,6.2311590898218299,6.243977861774197]

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