Kamis, 24 September 2009

Measuring Risk with Monte Carlo Simulation

. Kamis, 24 September 2009

Monte Carlo simulations up to now regarded as the best simulation predicts the risk for its accuracy. How the origins of this simulation, the mechanism and its use in the financial world?

Origin Discovery
Credit invention Monte Carlo method is often given to Stanislaw Ulam, a Polish mathematician. Ulam is known as the man who designed the hydrogen bomb with Edward Teller in 1951. Meanwhile, he himself found the Monte Carlo method in 1946 while taking into account the probability of winning solitaire card game.

On the other hand, in the world of finance and financial mathematics, Monte Carlo method is very useful to do a valuation and analysis of the various instruments and portfolio investment. This method allows simulation of various factors that affect the value of uncertainty, so that then can determine the average value

Monte Carlo method was first introduced into the financial world by David B. Hertz in 1964, in the article "Risk Analysis in Capital Investment" in the Harvard Business Review. Furthermore, in the year 1977, Phelim Boyle is the first time using this simulation in the paper about Options.

Mechanism Simulation
Monte Carlo Mechanism Simulations are often used to predict a specific value, based on historical data collection. This method is one of many methods of trying to analyze uncertainty, where the objective is to determine how random variation, lack of knowledge, and errors, may affect the sensitivity, performance, or reliability of the modeled system.

This simulation is classified as a sampling method, because the input generated at random from the probability distribution, to simulate the sampling process of the actual population. Thus, here we are trying to choose the input distribution that best matches the data held. The data generated from this simulation and then presented as probability distributions (histograms) or converted to error bars, reliability prediction, tolerance zones, until the confidence interval.

The use of World Finance
Monte Carlo simulation is widely use in the financial world, especially in investment and investment instruments are complex and involve many factors. Here are some investments that uses Monte Carlo simulations:
Evaluation Project, can be used to estimate the cost of the project and the Net Present Value of the project. In NPV account, for example, cash flow is a very big role, and have a high uncertainty, so that the simulation is very useful.
stock option valuation, where the simulation generates thousands of possible price of the underlying stock, each of which is accompanied by exercises option value. Payoff is then direrata and discounted to the present, the current option value.
Valuation of bonds, where the uncertainty is simulated interest rates. At every possible interest rate movements, then there are the estimated yield curve and bond prices are different. Valuation done by the average of these prices, then the present value.
Quantifying the risk, such as Value At Risk, where the data is the portfolio data and historical market data, for measuring the risk of a portfolio.


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1 komentar:

Angga mengatakan...

wouwww.. risk management ... talking serious things here. Haha.. that's remind me to the old days when I was in risk management course. The calculations sucks :P

:)) ;)) ;;) :D ;) :p :(( :) :( :X =(( :-o :-/ :-* :| 8-} :)] ~x( :-t b-( :-L x( =))

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