Monte Carlo Simulation

In: Business and Management

Submitted By ajjuiitm
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Monte Carlo simulations and option pricing by Bingqian Lu Undergraduate Mathematics Department Pennsylvania State University University Park, PA 16802 Project Supervisor: Professor Anna Mazzucato July, 2011

Abstract Monte Carlo simulation is a legitimate and widely used technique for dealing with uncertainty in many aspects of business operations. The purpose of this report is to explore the application of this technique to the stock volality and to test its accuracy by comparing the result computed by Monte Carlo Estimate with the result of Black-Schole model and the Variance Reduction by Antitheric Variattes. The mathematical computer softwear application that we use to compute and test the relationship between the sample size and the accuracy of Monte Carlo Simulation is itshapeMathematica. It also provides numerical and geometrical evidence for our conclusion.


Introduction to Monte Carlo Simulaion

Monte Carlo Option Price is a method often used in Mathematical finance to calculate the value of an option with multiple sources of uncertainties and random features, such as changing interest rates, stock prices or exchange rates, etc.. This method is called Monte Carlo simulation, naming after the city of Monte Carlo, which is noted for its casinos. In my project, I use Mathematica, a mathematics computer software, we can easily create a sequence of random number indicating the uncertainties that we might have for the stock prices for example.


Pricing Financial Options by Flipping a Coin

A distcrete model for change in price of a stock over a time interval [0,T] is √ Sn+1 = Sn + µSn ∆t + σSn εn+1 ∆t, S0 = s (1) where Sn = Stn is the stock price at time tn = n∆t, n = 0, 1, ..., N − 1, ∆t = T /N , µ is the annual growth rate of the stock, and σ is a measure of the stocks annual price volatility or tendency to fluctuate. Highly volatile…...

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