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加中金融                                          Quant Corner 数量分析














    波动率模型发展回顾




    Harel Jacobson

    Quantitative Portfolio Manager at Oporto Delta 波动率投资经理(以色列)



















    大部分期权交易者在第一次做期权定价时可能与我的经历非常                                   Any option trader’s first interaction with option pricing was probably
    相似。我在开始做期权定价前先阅读完约翰·赫尔写的《期权,                                  quite similar to mine. My first interaction with option pricing was while
    期货和 其他衍生 产品》 。就是 那个期权定价公 式(Black-                             reading “Option, Futures, and other derivatives” (by John Hull). There
                                                                  it was, this option pricing formula (Black-Scholes) where I could just
    Scholes),我可以在 Excel中输入几个参数,运行几个公式并获                           put few parameters in excel, run few formulas and get an actual price of
    得期权的实际价格。这真是令人难以置信 … 我觉得自己刚刚中                                 an option. This was mind-blowing… I felt like I just hit the jackpot, I’m
    奖了,我快将成为交易期权的亿万富翁了!不过快 14 年过去了,                               going be a billionaire trading options.. Fast-forward 14 years and I’m
    我还不是亿万富翁,但是在我观察波动率模型的演变和成形的                                   not a billionaire, but along the way I watched volatility modeling evolves
    过程中,我怀疑量子力学和从业者在 20、30 年前就想到过这些                               and takes shape, which I doubt quants and practitioners thought about
    了。                                                            20–30 years ago…
                                                                  We tend to think that, like the big bang, there was nothing before Black-
    我们倾向于认为,就像宇宙大爆炸一样,Black-Scholes(1973)                         Scholes  (1973),  but  the  root  of  modern  quant  finance,  and  option
    之前是没有任何模型的。但是现代量化金融的根源,尤其是期                                   pricing in particular is actually dated back to 1900, when Louis Bachelier
    权定价实际上可以追溯到 1900 年。当时 Louis Bachelier 提出了                     presented his thesis “The theory of speculation” (it sounds better in
    他的论文“投机理论”—在法语中听起来更好。Bachelier 的期权                            French). Bachelier’s option pricing model, which was used mainly for
    定价模型主要用于法国政府债券的期权定价,与 Black-Scholes                           pricing options on French government bonds, exhibits great similarities
    期权定价模型有很多相似之处。两者都使用非常相似的价格动                                   to what we know today as Black-Scholes option pricing model. Both
    态和概率假设,输入参数和收益函数。                                             use  pretty  similar  price  dynamic  and  probability  assumptions,  input
                                                                  parameters, and payoff.
    那么,为什么 Bachelier 模型没有像 Black-Scholes 那样被广泛使                   So why isn’t Bachelier model as widely used and known as B&S?
    用并广为人知?这主要是因为原始模型是针对特定类型的资产
    开发的。期权是基于未来合约价差而非实际价格,因此其假设                                   Mainly because the original model was developed for a specific type of
    和底层资产是唯一的。                                                    asset, its assumptions and underlying assets are unique in a sense that
                                                                  the option is on spreads (on a future contracts), rather than actual price.
    与时尚和潮流不同,Bachelier模型并没有过时,我们将在100多                            Unlike  fashions  and  trends,  the  Bachelier  model  did  not  become
    年后的今天看到它如何仍然适用,例如考虑一下 2020 年 4 月的                             obsolete, and we will later see how it remains relevant even today, more
    石油价格波动。                                                       than a 100 year later… (hint: think about the oil move during April 2020)

    那么,Fischer Black 和 Myron Scholes到底发展了什么,使他们的                  So what did Fischer Black and Myron Scholes develop that made their
    期权定价理论成为现代量化金融的基石,并授予 Myron Scholes                           option  pricing  theory  to  be  the  cornerstone  of  modern  quantitative
    斯诺贝尔奖?                                                        finance (and awarded Myron Scholes a Nobel Prize)?









                                            CCFA JOURNAL OF FINANCE   June 2021
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