Machine Learning for Volatility Trading

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1 Machine Learning for Volatility Trading Artur Sepp 20 March 2018 EPFL Brown Bag Seminar in Finance

2 Machine Learning for Volatility Trading Link between realized volatility and P&L of quant strategies trading volatility Supervised learning & learning to rank for selecting best models for volatility forecast Supervised learning for stock volatility forecast at earnings releases Machine learning for risk management of aggregated option books 2

3 Machine Learning is applied to forecast volatility and risk Volatility Trading (Systematic) Risk Management of Volatility Books (Flow and Systematic) Risk-Premia Investing Why? Niche strategies for the buy side Most of risk is managed using traders heuristics Recognition and demand from institutional investors How? Learn to select top models with best forecast power Learn optimal riskhedging process from market data Learn to identify risk-profile and best regimes for strategy performance 3

4 Option payoff can be replicated by the dynamic delta hedging One-Step Delta-hedged P&L for short straddle = Theta P&L Gamma P&L = Option Time Decay - Realized Convexity 4

5 Forecast of realized volatility is applied to estimate volatility risk-premium Volatility Risk Premium = Implied Volatility Realized Volatility Short Vega P&L = Volatility Risk Premium * Option Vega Relative value trading: sell options with high expected spread, buy with low expected spread 5

6 Using volatility forecast for the statistical estimation of the option value (vs market price) Estimate each factor using volatility forecast and assign risk-premia (or cross-sectional ranks) Option Value = + Replication Costs (Realized Gamma) = Realized Volatility * Gamma + Transaction Costs (For delta trading)= Realized Gamma * Bid/Ask Costs + Gap Risk (Un-hedgable delta-risk)=price Crashes & Illiquidity + MTM Valuation Risk (Vega risk) = Changes in implied volatility 6

7 Classes of Volatility models for forecast of the realized volatility Sample space estimators GARCH models Bayesian parametric models Close-to-close, Intraday estimators (Parkinson ) Assume random walk for the volatility Garch (1,1), Asymmetric Garch, etc Apply long-term history with mean-reversion Continuous type models with priors for vol forecast Apply intraday high/low price data Hidden Markov Chain Models (HMC) Discrete states of volatility Classification problem in unsupervised machine learning 7

8 Designing tests to assess the predicative power of volatility models Cannot use P&L from strategies to avoid over fit 1. Delta-hedged option P&L is highly path-dependent: need to reduce sensitivity to lucky paths 2. Model forecast is linked to the hedging policy which itself depends on the volatility estimate (in contrast to linear buys/sell predictions) Compare model forecast at specified hedging policy to benchmarks: 1. Benchmark to close-to-close volatility for end of day hedging 2. Benchmark to tradable intraday high/low estimators (Dupire 2015) 3. Distribution tests for the stability of the forecast 8

9 Distribution tests for volatility normalized returns over forecast period: ( ) ( ) For the model with good predicative power, the sample distribution of Z(n): 1. Has a symmetric distribution close to Normal (0,1) 2. Standard deviation of 1 (unbiased forecast) 18% Close-To-Close Volatility Estimator for HY Bonds ETF 18% Hidden Markov Chain Volatility Estimator for HY Bonds ETF 16% 14% 12% Empirical Normal (0,1) 16% 14% 12% Empirical Normal (0,1) 10% 10% 8% 8% 6% 6% 4% 4% 2% 2% 0% Volatility normalized return 0% Volatility normalized return 9

10 Robust estimator provides tight bounds for volatility forecast No surprises in the volatility forecast Robust application for strategies using volatility targeting Volatility Normalized Returns for HY bonds ETF Markov Chain CloseClose MarkovChain LowerQuantile MarkovChain UpperQuantile CloseClose LowerQuantile 10

11 Applying Supervised Machine Learning to Rank Model implementation Test Design Performance Evaluation Ranking Selection Learning to rank N (>30) different volatility models for forecast M (>=1) statistical tests to assess the power of the model forecast The performance is evaluated regularly (annually, quarterly, monthly, etc) M ranks based on the statistical power of the tests at each performance evaluation Selection of the top model or a combination of top models Forecasting of the top model at next performance evaluation (learning to rank) 11

12 Top-3 models for the S&P 500 index using the normality test annually in walk-forward analysis Each model is numbered (1,2, ) Markov Chain models (31,32) are frequently on the top Intraday estimators (1-10) are also reliable Top 3 Estimators with Normality fit for Volatility Normalized Returns for S&P 500 index Top - 1 Top - 2 Top

13 Top-3 models for High Yield Bonds ETF using the normality test annually Stable ranks for Markov chain (31-32) and GARCH models (21-30) Top 3 Estimators with Normality fit for Volatility Normalized Returns for HY bonds ETF Top - 1 Top - 2 Top Dec Dec Dec Dec Dec Dec Dec Dec Dec

14 Stock daily returns and intraday volatility are extreme on earnings release days Learn to adjust and forecast volatilities around special days 30% 20% 10% Daily Returns & Earnings days for Amazon stock Daily Return Earnings Day Lower 1-std Quantile Upper 1-std Quantile 450% 400% 350% 300% 250% Intraday Volatility & Earnings days for Amazon stock Intraday Volatility Earnings Day Lower 1-std Quantile Upper 1-std Quantile 0% 200% -10% 150% 100% -20% 50% 0% -30% -50% 20-Mar-03 5-Dec Aug-04 8-May Jan Oct Jun Mar Nov Aug-09 2-May Jan-11 4-Oct Jun-12 7-Mar Nov-13 9-Aug Apr Jan Sep Jun-17 1-Mar Mar-03 5-Dec Aug-04 8-May Jan Oct Jun Mar Nov Aug-09 2-May Jan-11 4-Oct Jun-12 7-Mar Nov-13 9-Aug Apr Jan Sep Jun Mar-18

15 High weights are assigned for volatility forecast over earnings release days Implied weights can be inferred from the term structure of ATM implied volatility Realized/forecasted weights can be learned from historical data Applications to relative value in trading volatility over earnings releases 70% 60% 50% 40% 30% 20% 10% 1m At-the-money implied volatility for Amazon stock ATM 1m Volatility Pre - Earnings Day Median 70% 60% 50% 40% 30% 20% 10% Volatility Forecast for Amazon stock with Earnings impact Volatility Forecast Volatility with Earnings impact 0% 27-Jan Jan Jan Jan-14 6-Jan-15 1-Jan Dec Dec-17 0% Days to / from Earnings release date 15

16 30% 25% 20% 15% 10% 5% Machine learning for volatility forecast using intraday estimators Statistical map using estimated intraday volatility over past periods: Expected absolute value of return on earnings day = Scaling*Estimated Intraday volatility Absolute Daily Return and Running quantiles for Amazon stock Absolute value of Daily Return Mean Lower 1-std Quantile Upper 1-std Quantile Mean Realized Absolute Return 10.5% 10.0% 9.5% 9.0% Mean Realized Absolute Return vs Predictor for Amazon stock y = x R² = % 8.5% 7.0% 7.2% 7.4% 7.6% 7.8% 8.0% 8.2% 8.4% Predictor 16

17 Machine learning for volatility model selection is applied on asset class level Aggregation by Asset Class: 1. Stock Indices 2. Technology Stocks 3. Agricultural Futures 4. G-10 FX 5. Learning phase for tests 1, 2, walk-forward with regular evaluations: 1. Stock Indices: Rank1 (t1), Rank1(t2), Rank2(t1), Rank2(t2), RankM(t1), RankM(t2), 2. Query processing: Volatility forecast for the S&P 500 index on 6-March-2018 for next month for deltahedged volatility carry 17

18 Robust management of portfolio of live and Smaller likelihood of back-test overfit: back-tested strategies When a trading algo requires volatility forecast at time t, it is provided with the best forecast known at t Test for forecast evaluation are tuned to algo types: Signal for volatility carry delta-hedged: test for best prediction of intraday volatility Volatility-target allocation with monthly rebalancing: test for the normality of volatility-normalized returns Dynamic selection of volatility forecast for live strategies: Robust adaptation to regime-changes 18

19 Query: Learning to rank for processing queries by analogy for web search engines Fetch volatility forecast for the S&P 500 index on 6-March for next month for delta-hedged volatility carry Search engine: 1. Analyse the collection of available tests results and ranks 2. Output forecast from single model or a linear combination of models Evaluation of user satisfaction: 1. Use P&L realized by the querier strategy 2. Tune up tests importance for query (delta-hedged volatility carry vs volatility-target allocation) 19

20 Application to Business model in Option Trading Trade generation using systematic strategies with Machine Learning Identify exchange-traded options with the highest expected reward-to-risk ratio 1. Positions & Hedges 2. P&L Report 3. Aggregated Risk Report Option Book Trade generation from flow/exotic business Look for OTC options with highest commissions/margins Statistical risk model with ML 1. Model-defined risk (delta,vega, 2. Risk Aggregation on Book level 3. Stress testing on book level Valuation model for Risk Aggregated Risk Report with mark-to-market valuation adjustments using historical data Mark-to-Market Valuation Model 1. P&L Report 2. Margin Report 20

21 Option Book Risk Management using Machine Learning Delta risk Vega risk Gamma / Tail risk Driver: Change in the asset price Change in the implied volatility Second and large order changes Learn: - Scaling of delta for different assets - Aggregation on the index level - Vega aggregation at maturities/strikes - How delta impacts vega risk -Scenario/stress test analysis - Regime conditional risk 21

22 Low number of statistical risk factors (2-3) explain vega and delta risk Apply PCA on changes in price and implied volatility surface % Portion of variance explained by components for changes in the implied volatility surface S&P500 Index AMZN stock 100% 80% 60% 40% 20% 86% 89% 92% 94% 95% 0% Number of Principal Components 22

23 Delta to Vega risk mapping Learn how changes in volatility are influenced by changes in the underlying asset Strong negative beta for short dated options Changes in 1m ATM volatility predicted by daily % changes in S&P 500 index y = x R² = % 20% 10% -10% -20% -30% -15% -10% -5% 0% 5% 10% 15% 20% 0% ATM volatility S&P 500 Beta 1m 2m 3m 6m 1y Expiry month 23

24 Adjustment of delta for Vega Market-based prediction for Vega risk from delta = Skew * Price Change Volatility skew beta is applied to hedge for the contribution to vega risk from the delta Changes in 1m ATM volatility predicted by Skew and daily % changes in S&P 500 index y = 1.25 x R² = % 20% 10% 0% ATM volatility Skew Beta -10% -20% -30% -15% -10% -5% 0% 5% 10% 1.2 1m 2m 3m 6m 1y Expiry month 24

25 Big Picture Investing: Learning the convexity profile of quant investment strategies Tail risk HF index (CBOE): positive tail convexity & negative delta = long implied volatility Short S&P 500 strangle (CBOE Condor): negative convexity = short realized volatility Trend-following CTAs (CG): positive tail convexity = long low-frequency realized volatility Monthly Returns on Hedge Fund strategies vs S&P Tail Risk HF Index y = x x R² = Short OTM puts and calls y = x x R² = SG Trend-following CTA y = x x R² = % 10% 5% 0% -5% X=Monthly Return on S&P500 Index -10% -20% -15% -10% -5% 0% 5% 10% 15% 25

26 Allocator for portfolio of quant strategies: learning regimes in which strategies outperform Top-down allocator using regime-based inference Bottom-up allocator using scenario analysis and clustering S&P500 SG Trend-following CTA Short OTM puts and calls Tail Risk HF Index $1 NAV time series

27 Conclusions: Machine Learning for volatility trading Machine learning for volatility model selection Query processing Applications for quant algo trading and asset allocation Apply a large number of models for vol prediction Rank models using specified tests Aggregate ranking on the level of asset classes Rank factors for prediction of covariance matrices Select the best model or their combination for the customised response to the query Query for the volatility forecast Apply the volatility forecast for strategy execution Refine queries based on feedback from strategy 27

28 References to personal work Optimal delta-hedging strategies for discrete hedging with transaction costs When You Hedge Discretely: Optimization of Sharpe Ratio for Delta-Hedging Strategy under Discrete Hedging and Transaction Costs Computing option delta consistently with empirical dynamics Empirical Calibration and Minimum-Variance Delta Under Log-Normal Stochastic Volatility Dynamics Volatility Modelling and Trading Diversifying Cyclicality Risk of Quantitative Investment Strategies 28

29 Disclaimer All statements in this presentation are the author personal views and not those of Julius Baer This presentation does not constitute investment advice 29

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