These stochastic processes are well known processes in financial engineering.
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| Short the samples in the window and omit r first samples and s last samples full text » |
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| The Black Karasinski for the short term interest rate 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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| Chain rule for sequences of random variables full text » |
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| This is the Clewlow and Strickland jump-diffusion mean-reversion SDE. This process is used to describe processes in the energy markets. full text » |
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| Constant elasticity of volatility. full text » |
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| Correlation coefficient full text » |
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| Cox-Ingersoll-Ross interest rate model full text » |
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| Generalized Auto-Regression Conditional Heteroskedacity (GARCH) stochastic volatility model. full text » |
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| General stochastic differential equation full text » |
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| The Geometric Brownian describes the most widely used model in finance. It is used to simulate the stochastic behaviour of stocks, currencies, futures.
The value of this process is strick positive, St cannot get below zero. full text » |
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| Heston stochastic volatility model. full text » |
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| The Hull-While model is an extended version of the Vasicek model. The short term interest rate is normal distributed, and is mean reverting. full text » |
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| The Merton jump-diffusion process is an extension to geometric Brownian motion. full text » |
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| Normal random variables full text » |
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| The Ornstein-Uhlenbeck process is the most common mean reverting stochastic process. full text » |
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| Orthogonal r.v.'s full text » |
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| Random process X(t) full text » |
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| Note that the variance of sample mean is n-time smaller than the one of a single sample. full text » |
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| Sample variance full text » |
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| The Schwartz type 1 model is a log price Ornstein-Uhlenbeck stochastic process. full text » |
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| Swartz type 2 stochastic process is a two-factor process. The first factor is the spot price, the second factor a instantaneous convenience yield. 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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| The Vasicek stochastic process full text » |
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