如果你也在 怎样金融数学Financial Mathematics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。金融数学Financial Mathematics是将数学方法应用于金融问题。(有时使用的同等名称是定量金融、金融工程、数学金融和计算金融）。它借鉴了概率、统计、随机过程和经济理论的工具。传统上，投资银行、商业银行、对冲基金、保险公司、公司财务部和监管机构将金融数学的方法应用于诸如衍生证券估值、投资组合结构、风险管理和情景模拟等问题。依赖商品的行业（如能源、制造业）也使用金融数学。 定量分析为金融市场和投资过程带来了效率和严谨性，在监管方面也变得越来越重要。
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我们提供的金融数学Financial Mathematics及其相关学科的代写，服务范围广, 其中包括但不限于:
- 随机微积分 Stochastic calculus
- 随机分析 Stochastic analysis
- 随机控制理论 Stochastic control theory
- 微观经济学 Microeconomics
- 数量经济学 Quantitative Economics
- 宏观经济学 Macroeconomics
- 经济统计学 Economic Statistics
- 经济学理论 Economic Theory
- 计量经济学 Econometrics
经济代写
数学代写|金融数学作业代写Financial Mathematics代考|Stock-Returns
The question of the long memory of stock returns has a long history. Mandelbrot (1971) first suggested that returns exhibit a long-range memory. Initial tests based on rescaled range $(\mathrm{R} / \mathrm{S})$ analysis seemed to prove that there is effectively some long-range memory of returns. Lo (1991) criticized tests based on $\mathrm{R} / \mathrm{S}$ analysis, observing that these tests were very sensitive to the short-term component; he introduced a modified $\mathrm{R} / \mathrm{S}$ test. Using this modified test, Lo reached a negative conclusion. But it was later observed in Teverovsky et al. (1999) that Lo’s modified $\mathrm{R} / \mathrm{S}$ test was too conservative. The authors find evidence of long range memory in the CRSP files but they find that the low value of the Hurst exponent $(\mathrm{H}=0,6)$ makes this conclusion uncertain.
Willinger et al. (1999) caution against using one single test to reach a conclusion regarding long-range memory. Ultimately, using a battery of tests, these authors conclude that there is not much evidence that returns have long-memory properties. They found that the decay of autocorrelation of individual stock returns was very rapid. However, absence of autocorrelation of returns does not imply absence of autocorrelation of non linear functions of returns. In particular, the absolute value of returns and power functions of absolute returns show strong autocorrelation. In other words, the sign of returns is basically unpredictable but the magnitude of returns is predictable.
数学代写|金融数学作业代写 Financial Mathematics代考|model volatility
This phenomenon is related to the well-known clustering of volatility, which means that extended periods of high volatility are followed by extended periods of low volatility. Clustering, however, is not equivalent to autocorrelation. Empirically it was found that the autocorrelation function of volatility decays as a power law.
The first attempt to model volatility was made by Engle (1982), with the introduction of the autoregressive model of conditional volatility now known as the autoregressive conditional heteroscedasticity (ARCH) model. Engle demonstrated that the ARCH model can represent a stationary process where, however, conditional volatility is time-dependent.
Suppose returns $r_{t}$ are represented by a factor model
$$
r_{t}=\mu+\beta_{1} f_{1 t}+\cdots+\beta_{k} f_{k t}+u_{t}
$$
where the $\beta_{i}, i=1, \ldots, k$ are constant factor loadings, $f_{i t}, i=1, \ldots, k$ are the factors and $u_{t}$ are the residuals which are normally distributed with conditional variance $\sigma_{t}^{2}$
The $\operatorname{ARCH}(p)$ model is written as:
$$
\sigma_{t}^{2}=\alpha_{0}+\alpha_{1} u_{t-1}^{2}+\cdots+\alpha_{p} u_{t-p}^{2}
$$
It is a deterministic model of volatility in the sense that volatility is a deterministic function of past errors.
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