Equations for generating random samples and paths from well known distributions and stochastic processes that are used in finance.
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| The Brownian Bridge is used to generate new samples between two known samples of a Brownian motion path. full text » |
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| The Schwartz type 1 model is a log price Ornstein-Uhlenbeck stochastic process. The calibration can be done through a regression of the logprices as described in the above equation. full text » |
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| This transform is used to generate a exponential distributed samples from a uniform distributed variable. full text » |
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| This is the Box-Muller method (the polar form version) for generating two standard normal (Gaussian) distributed variables using two uniform distributed variables. full text » |
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| This transform is used to generate Pareto distributed samples form uniform distributed samples. full text » |
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| This equation is used to generate scenarios that follow the Ornstein-Uhlenbeck process. This equation is exact.
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| Simulating geometric Brownian motion. This equation is the exact solution of the geometrix brownian motion SDE. full text » |
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| Simulating geometric Brownian motion with a cash dividend before T. full text » |
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| Simulating geometric Brownian motion with a stock dividend. full text » |
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| Simulating geometric Brownian motion with multiple cash dividend in the simulation step to T. full text » |
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| This equation is the exact solution of the one-factor Vasicek interet rate model. In this model interest rates are Normal distributed, and thus can become negative. full text » |
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| The Schwartz type 1 model is a log price Ornstein-Uhlenbeck stochastic process. Monte Carlo simulation of the model can be done using the equation above. The above equation is an exact solution of the model, this means that the distribution of the simulation is exact, and that time steps can be any size. full text » |
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