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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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first, there is a formula for the continuously monitored case. second, if you use log coordinates the Euler discretization is exact so this should be done. third, the convergence for discretely monitored to continuously is actually very slow so you will need a lot of steps. fourth, it's actually better to draw the hitting time to the barrier rather than ...


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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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Monte Carlo simulation in the context Financial Modeling refers to a set of techniques to generate artificial time series of the stock price,volatility and interest rate and... overtime, from which option prices can be derived. There are several choices available in this regard. The first choice is to apply a standard method such as the Euler, Milstein, or ...


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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


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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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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 ...


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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) ...



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