Page 34 - CCFA Journal - Fourth Issue

Quant Corner 数量分析
在过去几十年里，到底发生了什么使得从业人员觉得波动率是
非常粗糙的？
根据那些认为波动率是粗糙的人的说法，粗糙之处在于市场的
微观结构和动态性，由订单流的分布和行为所产生。近年来，
大多数订单流都是高频的，这一事实使其更加明显。
市场微观结构背后的理论是，买单产生更多的买单，卖出订单
产生更多的卖单，但卖出订单对订单簿和基础现货产生更大的
影响，即流动性不对称的“杠杆效应”。市场微观结构的另一
个特征是，市场上的大多数订单发生在市场参与者之间（交易
公司），而不是最终用户。
最近几年的可能是最重要的发展是计算速度的迅速提高，如量
子计算，低延迟基础结构和强大的数据库只是其中的一些发展。
粗糙波动率模型无法直接计算，如 Black-Scholes，Heston，
SABR，因为它们是非马尔可夫模型，缺乏记忆/独立性。因此
需要使用蒙特卡洛模拟来计算这些模型。特别是对于需要快速
结果/价格的从业者而言，MC 模拟是耗时的过程。
粗糙波动率的应用
自从 2014 年首次亮相以来，“粗糙波动性”研究一直呈指数级
增长。论文和应用程序经常被发表。下面是波动率建模领域的
一些有趣的应用程序：
1. 使用赫斯特（Hurst）指数估计波动率的阶段性。到目
前为止，赫斯特（Hurst）指数是时间序列自相关的度
量。实证研究表明，该指数大多数时候都保持在非常
低的水平上相对稳定（Gatheral 等人发现，对于长期指
数而言，H = 0.13 的股票指数），这意味着波动率在正
常市场中表现出强劲的均值回归。从历史上讲，在财
务压力时期，该指数往往会显着上升，因此，我们可
以将该指标用作波动率阶段性变化的信号。
2. 模拟股票的波动率套利。根据 Glasserman等人（2018）
发表的论文，波动率套利策略是具有剧烈波动率的多
头股票和具有平稳波动率的空头股票赚取了超额收益。
3. S＆P500 / VIX 波动率微笑联合校准。这可能是粗略波
动性研究领域中的最大成就。由于 S＆P500 / VIX 的动
态处于美国股票市场的中心（有人说现代金融的中
心），因此它成为定量研究人员和从业人员的极大兴
趣所在。根据 2020 年初的最新发现，Julien Guyon 的研
究和尝试解决 S＆P500 / VIX 波动率微笑联合校准的尝
试被证明是成功的。这是一项重大突破，因为过去使
用不同的动力学和模型进行的尝试未能成功地准确地
共同校准两个波动面。这项研究表明，粗略波动率的
假设可能要优于假定用来描述波动率动力学的其他波
动率动力学。
CCFA JOURNAL OF FINANCE
Page 34 第34页
加中金融
So what has changed over the last few decades that makes practitioners
think that volatility is rough?
According to those who believe that volatility is rough, the roughness
lies in the market microstructure and dynamic (order flow distribution
and behavior). The fact that in recent years most order flows are HFT
(high-frequency) just makes it more pronounced.
The theory behind the market microstructure is that buy orders generate
more buy orders, and sell orders generate more sell orders, BUT sell
orders have more impact on the order book and underlying spot
(liquidity asymmetry , “leveraged effect”). Another feature of the market
microstructure is that the most orders in the market are between market
players (trading firms, not end users).
The last, and probably the most important development that took place
over the last few years, has been the rapid increase in computation speed
(quantum computing, low-latency infrastructure , and strong numerical
libraries are only some of these developments) . Rough Volatility
models cannot be calculated directly (like B&S, Heston, SABR), as they
are non-markovian (i.e. lack memory/independent), so one needs to use
Monte Carlo simulation to compute these models. MC simulations are
time consuming processes (especially for practitioners who need fast
results/prices).
Rough Volatility applications
Since it made its debut in 2014, the Rough Volatility research has been
growing exponentially. Papers and applications are frequently being
published (link to the literature in the appendix). Here are a few
interesting applications of this field of volatility modeling:
1. Estimating volatility regime using the Hurst index — As we know
by now, the Hurst index is a measure of the timeseries
autocorrelation. Empirical studies have shown that this index stays
relatively stable at a very low level most times (Gatheral et. al found
that for equity indices H=0.13 on long term horizon), this means
that volatility exhibits in normal markets strong mean reversion.
Historically speaking, during period of financial stress that index
tends to rise significantly, therefore, we can use that indicator as a
signal of change in volatility regime.
2. Modeling volatility arb in stocks — as per paper published by
Glasserman et He(2018), volatility arb strategies that were long
stocks with rough volatility and short stocks with smooth volatility
earned excess return.
3. S&P500/VIX smile joint calibration — Probably the biggest
achievement in the field of rough volatility research. As
S&P500/VIX dynamic is in the epicenter of US equity market (and
some would say the epicenter of modern finance), it’s the subject
of huge interest by quant researchers and practitioners. Julien
Guyon’s research and attempt to solve the joint smile calibration
of S&P500/VIX proved to be successful (as per his latest findings,
dated to the beginning of 2020). This is a major breakthrough, as
past attempts, using different dynamics and models were not
successful in accurately calibrating the two volatility surfaces jointly.
This research shows that the assumption of rough volatility is
probably superior to other volatility dynamics that were assumed
to be describing the volatility dynamic.
June 2021