Monte Carlo Simulation

simulation codes

• rand follows uniform distribution between [0,1], randn follows normal distribution between [0,1].

• rand(2,1), rand(2)

• his(rand(100000,1))

• icdf

• icdf('Normal', rand(100000,1), 0.3,0.4)

• A=icdf('exp', rand(100000,1), 0.5)
  hist(A)

Multivariate Random Number

• mvnrnd([2;4][2 1;1 3])
• mvnrnd([2;4][2 1;1 3],5)
• A=mvnrnd([2;4][2 1;1 3],50000)
  plot(A(:,1), A(:,2),'d')

** Simulating period by period**

Code

• Path is a matrix, in the last command, do remember to write "." after the Path(;,i), or Matlab will think it as a whole matrix transform, rather than for each element specified.
• "Nsim" is number of simulation

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** The simulated discounted present value **

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Statistic Inference

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Exercise

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Variance Reduction

• Antithetic Algorithm

Example

• Control Variable