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5

You don't need to use the Sobol sequence to generate quasi-random numbers in MATLAB. We know the Heston model is represented by the bi-variate system of stochastic differential equations (SDE): \begin{align} & d{{S}_{t}}=rS_tdt+{\sqrt\upsilon_t} d{{W}_{1}}(t) \\ & d{{\upsilon}_{t}}=\kappa(\theta-\upsilon_t) ...


3

I have approximate the integrals by Monte Carlo Method but you can use several method such as Newton-Cotes formulas and Gaussian quadrature. Function Example Solutions Call = 34.0976 Put = 4.8941 Parameters were extracted from Jianwei Zhu(2008),Page 10,Table 4


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the LIBOR market model the Heston model -- Euler and Milstein are actually bad for this and much more sophisticated methods are necessary local volatility models


2

1. weighted Milstein Scheme We assume $\{X_t\}_{t\geq0}$ described by the following stochastic differential equation $$dX_t=\mu(t,X_t)dt+\sigma(t,X_t)dW_t\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$$ Under the Ito version of this scheme Equation $(1)$ becomes $$dX_{t+\Delta t}=X_t+[\alpha\,\mu(t,X_t)+(1-\alpha)\mu(t+\Delta t,X_{t+\Delta t})]\Delta t+\sigma\sqrt{\Delta t ...


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Well, log-normality does not allow you to have negative earnings and companies do have negative earnings. I suggest you to download the earnings data and perform a Jarque-Bera test for normality.


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First I provide a brief description of Halton sequences. A Halton sequence is a deterministic sequence of numbers that provides well-spaced 'draws' from an interval and provides negative correlation between simulated probability for individuals. Generation is based on a prime number Sequence is constructed based on finer and finer prime-based divisions of ...


1

It is straightforward to include dividends into the model if it can be assumed that the dividend payment is a continuous dividend yield, $q$. Under $Q$ measure , In the Black-Scholes Model, Heston Model and etc, $r$ is replaced by $r − q$., Here, We are going to simulate underlying asset in the Black-Scholes model by Milstein Method.Indeed, we assume ...



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