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[null,"Description\n\nThis workbook uses NAG Library routines to perform a simple Monte Carlo simulation.  A Call option is priced in the Black Scholes model, i.e. using Geometric Brownian motion.  Confidence intervals for the price are also computed.  Finally, the price and the confidence intervals are plotted as a function of the Monte Carlo sample size.  The classic \"square root\" convergence is observed, as the confidence intervals converge to the true price as 1/sqrt(n).\n\nAlthough this is a simple example, the ideas it illustrates are very general.  Using this example as a template, customers can embed NAG Library functionality into Excel to solve advanced and computationally intensive problems while keeping all the benefits of using Excel as a front end."]

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[]
[]
[null,null,null,null,null,null,null,null,"Monte Carlo Option Pricing"]
[]
[null,null,null,null,null,null,null,"We price a call option in the Black Scholes model using simple Monte Carlo.  Note that the confidence intervals decay as the square root of the number of Monte Carlo samples.  This is the main problem with Monte Carlo"]
[]
[null,null,null,"Inputs"]
[]
[null,null,null,"S0 :",100]
[null,null,null,"Strike :",80]
[null,null,null,"Sigma :",0.3]
[null,null,null,"Interest rate :",0.05]
[null,null,null,"Dividend yield :",0.02]
[null,null,null,"Time to maturity :",1]
[null,null,null,"Num. MC samples :",1000]
[null,null,null,"Plot Interval :",10]
[]
[]
[null,null,"Output"]
[]
[null,null,null,"Monte Carlo Price :",25.864226356130015]
[null,null,null,"True price :",24.783318682677873]
[null,null,null,"Conf. Interval Up :",28.32389090035495]
[null,null,null,"Conf. Interval Dwn :",23.404561811905079]
[null,null,null,"Conf. Intval Width :",{"$f":"ciup-cidown","v":4.9193290884498708}]