Monte Carlo Simulation
Monte Carlo, Monaco, hosts casinos where games of chance, such as slot machines, are played. Although a slot machine occasionally spews out chunks of tokens to lucky patrons, it, in the long run, earns a predictable fortune for the casino owner. A scientist usually devices her games of chance with various tunable parameters. After many plays, she compares the outcome with that of the real experiment. By changing the values of the parameters, she hopefully reproduces in the game the experimental result. This way, scientists gain a better knowledge of the world. In other cases where experiments are hard or expensive to carry out, simulation is the only alternative. The method of simulation or calculation that involves sampling from random numbers is coined Monte Carlo method. We show how to generate specific distributions from a uniform random distribution. We introduce and implement in the example a stochastic-volatility jump-diffusion process to simulate the complex dynamics of the price of a financial asset.
KeywordsPetroleum Covariance Volatility
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References and Further Reading
- Textbooks on probability and statistics are, G. Cowan, “Statistical Data Analysis”, Oxford University Press, Oxford (1998)Google Scholar