前几天看到了 Quant of the Year 2021发布的新闻，颁发 （写 The Volatility Surface - a practioner's guide 和 ，他们研究的主题是 The Rough Volatility。
Jim Gatheral 当他收到随机波动率的局限性时，他很早就意识到了这一点（fractional Brownian motion）当他惊呼这是上帝模型（God's model）。以此为基础 rough volatility 传统布朗运动无法实现的各种模型都能非常准确地捕捉到波动市场。
下面简单回顾一下这个 20 年做怎么办？
：The quadratic rough Heston model and the joint S&P 500/Vix smile calibration problem
The application of the rough vol model will make the Vix option market become more efficient. --Huaming Jin, Luoshu Investments
新闻链接：
https://www.risk.net/awards/7736196/quants-of-the-year-jim-gatheral-and-mathieu-rosenbaum
Quant 和 Trader 长期困扰的一个问题是 S&P 和 VIX 期权的目标是 S&P500 该指数，但两个期权市场的隐含波动性不同。如果有一个模型可以同时校正 S&P 和 VIX 该模型可以识别期权波动平面的良好交易机会。
之前Julien Guyon 其实这个问题已经解决了，但是用的是一个 non-parametric 模型。
Rosenbaum 参加了 Guyon 演讲立即实现了这项工作的重要性，然后和 Gatheral 发现用 模型也可以完美校正 SPX-VIX 联合校正。
：Libor replacement: a modelling framework for in-arrears rates
Interms of topicality, applicability and broadness, it doesn’t get much bigger than this. --Leif Andersen, Bank of America Merrill Lynch
新闻链接：
https://www.risk.net/awards/7204391/quants-of-the-year-andrei-lyashenko-and-fabio-mercurio
本论文主要用于解决来替代痛点，即利率范式不同
前者是（backward-looking）只有在终止日才能知道利率的价值
后者是（forward-looking）利率，在起始日就已经知道其值
解决方案是设计一个「前瞻型」的。具体来说，在范围内[Tn-1, Tn] 上用 Fn(t) 代表这种前瞻性利率，它和 LIBOR MarketModel(LMM) 里的Ln(t) 范式相同，都在Tn-1上定盘，利率有效期为[Tn-1, Tn]。
但在定价利率复杂的产品时，需要一系列的产品Fn(t)此时，我们需要在一定的测量下推出每一个建模Fn(t) (n = 1, 2, ..., N)随机微分方程（Stochastic Differential Equation, SDE）。类比LMM 的叫法，对Fn(t)建造的模型叫做 FMM，全称是 Forward Market Model。
关于 FMM，我还写了三篇文章供参考。
：Curve Dynamics with Artificial Neural Networks
：Evolutionary Algos for Optimising MVA
Quants these days tend to maintain expertise in specific fields. With Alexei, his expertise in multiple, unrelated fields gives him a broader perspective and makes him a great researcher. -- Alexander Sokol
新闻链接：
https://www.risk.net/awards/6159246/quant-of-the-year-alexei-kondratyev
事实上，机器学习在金融中的应用主要是买方 (buy side), 比如私募或者基金， Alexei 主要贡献是在银行等卖方中找到两个应用：
使用人工神经网络 利率曲线与商品远期曲线之间的动态关系与自动编码器有关。【】
用遗传算法 (Genetic Algorithm, GA) 和粒子群优化 (Particle Swarm Optimization, PSO) 减少银行压缩交易保证金 (margin)。两者都是进化算法，GA 主要在离散变量空间 (比如货币 currency, 交易对手 counterprty) 找最优解，而 PSO 主要在连续性变量空间 (比如年限 tenor, 本金 notional) 找最优解。【】
论文还要好好读，至少现在我觉得第一篇的 input 的选择就有些不合理，可能犯了数据窥探 (data snooping) 的错误。Alexei 目前还在研究量子计算 (Quantum Computing)，和 NASA 合作把量子计算应用在一个含 个资产的组合优化上，节省了一半的计算时间。(是不是有点小题大做了？)
：Does Initial Margin Eliminate Counterparty Risk
They looked at the entire complexities of the margining process and modelled it mathematically. They looked at things from first principles and the result was amazing. -- Alexei Kondratyev
新闻链接：
https://www.risk.net/awards/5371021/quants-of-the-year-leif-andersen-michael-pykhtin-and-alexander-sokol
：Cleaning Correlation Matrices
It is really more of a physics approach, to let the data speak. A lot of models used in mathematical finance seem to be more driven by their convenience and the possibility to answer a question with a number, rather than taking the time and thinking about the problem. -- Bouchaud
新闻链接：
https://www.risk.net/risk-magazine/analysis/2479713/quant-of-the-year-jean-philippe-bouchaud
：The Free Boundary SABR Natural Extension to Negative Rates
：FVA for General Instruments
：Backward Induction for Future Values
In all his papers there is a clear practical problem, amazing mathematics and practical implementation. I think the combination of those three elements is really quant work at its best. -- Paul Glasserman
新闻链接：
https://www.risk.net/awards/2442477/quant-of-the-year-alexandre-antonov
：Funding Strategies, Funding Costs
The way they have approached the problem is revolutionary. They have gone back to basics and modified the Black-Scholes PDE. And because it is intuitive, it is very revealing in that you can see the cashflows in a very transparent way. -- Andrew Green
新闻链接：
https://www.risk.net/derivatives/2387793/quants-year-christoph-burgard-and-mats-kjaer
Exposure under Systemic Impact
Systemic risk is at the forefront of everyone’s mind but is notoriously difficult to quantify. Pykhtin’s clear and pragmatic approach goes a long way towards setting a rigorous framework to measure and control it. -- Vladimir Piterbarg
新闻链接：
https://www.risk.net/awards/2320285/quant-year-michael-pykhtin
I see this as an important part of my role – communicating these technical details, This dialogue between industry and regulator is an increasingly valuable function as rules and guidelines get more technical. It’s familiar to Pykhtin – from both sides.
：Being Particular about Calibration
：Cutting CVA's Complexity
It’s not complicated, actually. Using Malliavin is no harder than using the Itô lemma or the Girsanov theorem. -- Pierre Henry-Labordère
新闻链接：
https://www.risk.net/awards/2232028/quant-of-the-year-pierre-henry-labordere-societe-generale
：Volatility Interpolation
：Random Grids
There are no fundamental laws handed down from God on clay tablets. I think there is still a tendency to see the world through models, forgetting they are only as good as their implementation. -- Jesper andreasen
新闻链接：
https://www.risk.net/awards/2133160/quants-year-jesper-andreasen-and-brian-huge-danske-bank
：Funding Beyond Discounting Collateral Agreements and Derivatives Pricing
What Piterbarg is doing is rewriting Black-Scholes post-financial crisis. After the crisis, you can’t ignore the cost of funding in any asset class or you lose money. -- Alex Langnau
新闻链接：
https://www.risk.net/awards/1934297/quant-year-vladimir-piterbarg-barclays-capital
：A dynamic Model for Hard-to-Borrow Stocks
Short selling is a common scapegoat during financial crises. In 2008, the ban on short selling was also used as a form of protectionism for propping up the stock of financial firms. -- Marco Avellaneda
新闻链接：
https://www.risk.net/awards/1567801/quant-of-the-year-marco-avellaneda
：Smile Dynamics III
His idea of directly modelling the joint dynamics of the spot and variance swap volatility is theoretically sound and practically easy to implement. His quant of the year award is well deserved. -- Alexander Lipton
新闻链接：
https://www.risk.net/awards/1496978/quant-year-lorenzo-bergomi
：Calibrating and Pricing with Embedded Local Volatility Models
The most important moment of my career was my meeting with professor Dilip Madan. He is one of the few academics that are aware that the future does not behave like the past. -- Peter Carr
新闻链接：
https://www.risk.net/awards/1498261/quant-year-dilip-madan
：Smoking Adjoints Fast Monte Carlo Greeks
The adjoint method accelerates the calculation of Greeks via Monte Carlo simulation by, in essence, rearranging the order of calculations, as compared to the standard method. -- Paul Glasserman
新闻链接：
https://www.risk.net/awards/1498251/quants-year-paul-glasserman-and-michael-giles
：Time to Smile
The global skew is some sort of average of local skew. -- Vladimir Piterbarg
新闻链接：
https://www.risk.net/awards/1497820/quant-year-vladimir-piterbarg
：A Measure of Survival
Schönbucher is one of the most innovative researchers in credit and many of today’s practitioners have benefited from his insights. His work on CDS option pricing is typically focused and thorough, and will form the backbone of future work on the subject. -- Richard Martin
新闻链接：
https://www.risk.net/awards/1497632/quant-year-philipp-schonbucher
：Random Tranches
Gordy’s work in portfolio credit risk is both distinguished and topical, with many of his papers being among the cornerstones of modern credit risk management practices. His work at the Federal Reserve has been highly influential with academics and practitioners alike. -- Leif Andersen
新闻链接：
https://www.risk.net/awards/1498479/quant-year-michael-gordy-us-fed
：Black-Scholes Goes Hypergeometric
Peter has contributed more fundamental ideas to the area of mathematical finance in the past couple of years than anyone I am aware of. Peter lives, eats and breathes mathematical finance. -- Keith Lewis
新闻链接：
https://www.risk.net/derivatives/1506232/quant-of-the-year-peter-carr
：Taking to the Saddle
In credit risk modelling, he’s the most switched on person I know. -- Tom Wilde
新闻链接：
https://www.risk.net/awards/1506446/2002-winner-quant-year-richard-martin
：Jumping Smiles
：Static Barriers
无新闻链接
：Similarities Via Self-Similarities
无新闻链接
到处都下载不到他的论文，甚至都很难搜索出来。听说是关于介绍复杂衍生物的定价方法论，但是细节不清楚因此不评价。
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总结
这 20 年的年度宽客和他们得奖论文主要分成 (Market Risk)， (Credit Risk, XVA)，和这四大类，如下图所示：
从上表来看，研究市场风险的趋势在下降；研究估值调整，融资成本 (funding cost) 和保证金 (initial margin) 越来越多；研究机器学习的从今年刚开始有第一篇，按着大趋势以后会越来越多。
：2007 年的最佳论文 Smoking Adjoints: Fast Monte Carlo Greeks 真实好东西，这个 Adjoint 方法其实和机器学习里面的反向传播非常类似，这种反向求导数的方法统称 Adjoint Automatic Differentation, AAD，在金融和机器学习中有太多应用，比如百慕大期权蒙特卡洛求敏感度，比如组合层面的 XVA，比如深度神经网络的反向传播，只要求少量输出对大量输入的导数，AAD 在效率和速度上会让你重新认识这个世界。
想学习 Python 内容，可参考我的《三套 Python 精品课》。