科学网

 找回密码
  注册

tag 标签: 数理金融学

相关帖子

版块 作者 回复/查看 最后发表

没有相关内容

相关日志

数理金融学的范式危机与变革
gaohong5250 2019-12-2 10:39
【摘要】本文指出数理金融学将资产价格随时间演变的过程假设为随机变量,是导致数理金融学产生范式危机的根本原因。本文根据金融资产价格与时间一一对应的函数关系,使用样本函数范式和公理化方法重建了数理金融学的基本概念、基本定律和基本结论,建立了积分形式的随机游走模型,演绎推导出了可揭示金融资产价格运动规律的时间自相关函数和功率谱密度函数,从理论上证明了股票价格的可预测性,发现了隐藏在随机游走过程中的长期线性趋势。 一、引言 数理金融学是一门运用数学理论和方法研究金融市场数量关系及其变化规律的交叉性学科。金融市场大量的实证研究结果和案例分析表明,数理金融学建立的资产价格数学模型与经验事实不一致,不能正确描述资产价格波动现象并预测其变化趋势, 数理金融学价格模型及定价公式在金融领域中的广泛应用 是导致多次金融危机的罪魁祸首( Triana,2014 )。畅销书《黑天鹅》作者 Taleb 在《金融时报》上发表专栏文章,将数理金融学斥之为“破坏市场的伪科学”。 本文指出了导致数理金融学陷入严重危机的随机变量假设错误,并采用样本函数范式建立了积分形式的股票价格随机游走时间函数模型,演绎 推导出了时间自相关函数和功率谱密度函数,从理论上证明了股票价格的可预测性, 发现了隐藏在随机游走中的长期线性趋势。 二、危机现象 (一)价格模型与经验事实不符 早在 1900 年,数理金融学的奠基人、法国数学家 Bachelier 在其博士论文《投机理论》中,首先应用概率方法对股票价格随时间的变化规律进行研究,发现股票价格的变化是完全随机的,并用随机变量表示任一时刻的股票价格,建立了股票价格算术布朗运动模型。 1958 年,美国海军研究实验室的高能物理学家 Osborne 发现 Bachelier 的算数布朗运动模型存在股票价格会变为负数的理论缺陷,将其修改为几何布朗运动模型。 由于 Osborne 也假设股票价格为随机变量,因此几何布朗运动模型的数学期望为零,无法描述和解释股票价格波动中存在的长期线性趋势。为解决这一问题, Samuelson 给几何布朗运动模型增加了线性漂移项,建立了带漂移的几何布朗运动模型。但是,线性漂移项中的漂移率为常数,表明股票价格的短期收益率数学期望不为零,意味着股票市场中存在着确定性的盈利机会,与股票价格变化完全随机的观察现象和数理金融学“股票价格短期收益率均值为零”的实证研究结果不符。 此外,几何布朗运动模型假设股票短期收益率服从正态分布,与实际股票收益率呈现出的尖峰厚尾特征和中期随机跳跃现象不符,为了刻画这种小概率极端变化现象, Merton ( 2013 )又在几何布朗运动模型中增加了泊松跳跃过程,但仍然没有解决增加线性漂移项带来的问题。 (二)定价公式导致金融危机 1973 年, Black 和 Scholes 基于 Samuelson 的几何布朗运动模型,推导出了著名的 BS 期权定价公式。由于从理论上解决了金融衍生产品的定价问题, BS 期权定价公式对各种金融创新工具和金融创新产品的面世起到了重大的推动作用,直接导致了“第二次华尔街数学革命”,使金融市场获得了空前规模的发展。 让人意外的是, BS 期权定价公式的广泛应用,给金融市场带来了巨大的灾难。由 BS 期权定价公式衍生出的计算机股票交易策略,成为直接导致 1987 、 1997 和 2007 年三次重大金融危机的主要原因( Mackenzie , 2018 ),数理金融学因而陷入了严重的困境。一些经济学家多年来一直呼吁,几何布朗运动模型无法正确描述资产价格现象, BS 期权定价公式永远不应该使用。 三、危机根源 数理金融学在 100 多年的发展过程中,始终无法解决资产价格数学模型与事实不符的问题,究其原因,是将 金融资产价格与时间之间的数量关系错误地假设为随机变量。 《时代金融》, 2019 年第 8 期 数理金融学的范式危机与变革_高宏.pdf
1965 次阅读|0 个评论
[转载]破坏市场的伪科学
gaohong5250 2019-12-2 09:54
畅销书《黑天鹅》作者纳西姆·塔勒布在《金融时报》上发表了题为“破坏市场的伪科学”专栏文章,对数理金融学进行了严厉批判,我们从一次又一次的金融危机中得出一个结论:现代数理金融学理论的有效性与占星术一样不靠谱,数理金融学理论获得诺贝尔奖不仅仅是对科学的侮辱, 数理金融学理论 通过创造风险来危害金融系统,一直使金融体系面临崩溃的风险。 The pseudo-science hurting markets Last August, The Wall Street Journal published a statement by one Matthew Rothman, financial economist, expressing his surprise that financial markets experienced a string of events that “would happen once in 10,000 years”. A portrait of Mr Rothman accompanying the article reveals that he is considerably younger than 10,000 years; it is therefore fair to assume he is not drawing his inference from his own empirical experience but from some theoretical model that produces the risk of rare events, or what he perceives to be rare events. The theories Mr Rothman was using to produce his odds of these events were “Nobel-crowned” methods of the so-called modern portfolio theory designed to compute the risks of financial portfolios. MPT is the foundation of works in economics and finance that several times received the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. The prize was created (and funded) by the Swedish central bank and has been progressively confused with the regular Nobel set up by Alfred Nobel; it is now mislabelled the “Nobel Prize for economics”. MPT produces measures such as “sigmas”, “betas”, “Sharpe ratios”, “correlation”, “value at risk”, “optimal portfolios” and “capital asset pricing model” that are incompatible with the possibility of those consequential rare events I call “black swans” (owing to their rarity, as most swans are white). So my problem is that the prize is not just an insult to science; it has been putting the financial system at risk of blow-ups. I was a trader and risk manager for almost 20 years (before experiencing battle fatigue). There is no way my and my colleagues’ accumulated knowledge of market risks can be passed on to the next generation. Business schools block the transmission of our practical know-how and empirical tricks and the knowledge dies with us. We learn from crisis to crisis that MPT has the empirical and scientific validity of astrology (without the aesthetics), yet the lessons are ignored in what is taught to 150,000 business school students worldwide. Academic economists are no more self-serving than other professions. You should blame those in the real world who give them the means to be taken seriously: those awarding that “Nobel” prize. In 1990 William Sharpe and Harry Markowitz won the prize three years after the stock market crash of 1987, an event that, if anything, completely demolished the laureates’ ideas on portfolio construction. Further, the crash of 1987 was no exception: the great mathematical scientist Benoicirc;t Mandelbrot showed in the 1960s that these wild variations play a cumulative role in markets – they are “unexpected” only by the fools of economic theories. Then, in 1997, the Royal Swedish Academy of Sciences awarded the prize to Robert Merton and Myron Scholes for their option pricing formula. I (and many traders) find the prize offensive: many, such as the mathematician and trader Ed Thorp, used a more realistic approach to the formula years before. What Mr Merton and Mr Scholes did was to make it compatible with financial economic theory, by “re-deriving” it assuming “dynamic hedging”, a method of continuous adjustment of portfolios by buying and selling securities in response to price variations. Dynamic hedging assumes no jumps – it fails miserably in all markets and did so catastrophically in 1987 (failures textbooks do not like to mention). Later, Robert Engle received the prize for “Arch”, a complicated method of prediction of volatility that does not predict better than simple rules – it was “successful” academically, even though it underperformed simple volatility forecasts that my colleagues and I used to make a living. The environment in financial economics is reminiscent of medieval medicine, which refused to incorporate the observations and experiences of the plebeian barbers and surgeons. Medicine used to kill more patients than it saved – just as financial economics endangers the system by creating, not reducing, risk. But how did financial economics take on the appearance of a science? Not by experiments (perhaps the only true scientist who got the prize was Daniel Kahneman, who happens to be a psychologist, not an economist). It did so by drowning us in mathematics with abstract “theorems”. Prof Merton’s book Continuous Time Finance contains 339 mentions of the word “theorem” (or equivalent). An average physics book of the same length has 25 such mentions. Yet while economic models, it has been shown, work hardly better than random guesses or the intuition of cab drivers, physics can predict a wide range of phenomena with a tenth decimal precision. Every time I have questioned these methods I have been abruptly countered with: “they have the Nobel”, which I have found impossible to argue with. There are even practitioner associations such as the International Association of Financial Engineers partaking of the cover-up and promoting this pseudoscience among financial institutions. The knowledge and risk awareness we are accumulating from the current subprime crisis and its aftermath will most certainly not make it to business schools. The previous dozen crises and experiences did not do so. It will be dying with us, unless we discredit that absurd Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel commonly called the “Nobel Prize”. 原文: 《金融时报》-破坏市场的伪科学( Nassim Taleb ).pdf
2105 次阅读|0 个评论

Archiver|手机版|科学网 ( 京ICP备07017567号-12 )

GMT+8, 2024-5-22 04:49

Powered by ScienceNet.cn

Copyright © 2007- 中国科学报社

返回顶部