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1、Global Quantitative and (2) carry (aka roll cost). While volatility is mean- reverting, carry tends to be stable and is negatively correlated to changes in volatility. We construct a Dynamic Linear Model to capture these relationships, and predict the PnL using the Kalman Filter algorithm. Using the
2、 expected PnL as a trading signal, we adjust our long/short positions in the VIX/VSTOXX volatility spread strategy.VIX/VNKY strategy: Hedging for a spike in VNKY Investors concerned about a spike in VNKY could consider our VIX/VNKY strategy that shorts VIX and longs VNKY, with systematically adjuste
3、d exposures based on our Dynamic Linear Model. This strategy offers protections during volatile periods in the NIKKEI and earns decent carry from the short VIX position during tranquil markets.Cumulated PnL (in vol points) of our systematic VIX/VSTOXX strategy (left) and VIX/VNKY strategy (right): T
4、he black line shows the total PnL after t-cost, where total PnL is the sum of PnL due to change in volatility (green) and carry (orange)Source: J.P. Morgan Quantitative and Derivatives Strategy, Bloomberg.Completed 31 Jan 2018 12:29 AM HKT Disseminated 31 Jan 2018 12:29 AM HKT2Global Quantitative th
5、e strategy is rebalanced daily, and we have accounted for transaction costs Since 2010Since 2014Variance of long-term mean for volatility spreadStartEndAnnualized ReturnsAnnualized VolIRMax DrawdownHit RatioSortino RatioCalmer Ratio Since 2010 0.000052010-01-052018-01-198.6%9.2%0.938.4%45.8%0.101.02
6、 0.00012010-01-052018-01-198.9%9.2%0.967.4%45.9%0.101.21 0.00052010-01-052018-01-197.6%9.2%0.838.9%45.5%0.090.85 0.0012010-01-052018-01-197.9%9.3%0.859.6%45.3%0.090.83Since 2014 0.000052014-01-022018-01-1910.0%10.1%0.996.5%46.2%0.101.55 0.00012014-01-022018-01-1910.2%10.2%1.006.4%45.9%0.101.59 0.000
7、52014-01-022018-01-199.7%10.0%0.977.1%45.1%0.101.36 0.0012014-01-022018-01-199.4%10.1%0.937.2%45.2%0.101.30Source: J.P. Morgan Quantitative and Derivatives Strategy, Bloomberg25Global Quantitative transaction costs have been included (0.5 for VNKY, 0.02 for VIX)Source: J.P. Morgan Quantitative and D
8、erivatives Strategy, Bloomberg8One could argue whether our strategy should be flexible so as to allow a short position in VNKY if it is preferable. We will look at a long/short strategy on p.37, but it turns out that high transaction costs in VNKY futures will hurt performance.28Global Quantitative
9、the two charts show the same information the left one shows the scatter plot for all datapoints, while the right one shows a smooth curve by aggregating similar levels of volatility spread into 20 bins along the x-axisSource: J.P. Morgan Quantitative and Derivatives Strategy, Bloomberg29Global Quant
10、itative we scale down the short exposure in VIX if the signal is very positive and scale up the long exposure in VNKY if the signal is very negativeSource: J.P. Morgan Quantitative and Derivatives Strategy, Bloomberg33Global Quantitative the strategy is rebalanced monthly, and we have accounted for
11、transaction costs (0.02 for VIX and 0.5 for VNKY)Variance of long-term mean for volatility spreadStartEndAnnualized ReturnsAnnualized VolIRMax DrawdownHit RatioSortino RatioCalmer Ratio Since 2012-09 0.00012012-09-042018-01-196.1%8.3%0.748.0%53.3%0.070.76 0.00052012-09-042018-01-196.5%8.5%0.768.2%53
12、.9%0.070.79 0.0012012-09-042018-01-196.2%8.6%0.729.3%54.2%0.070.67 0.0052012-09-042018-01-195.9%8.9%0.6710.8%54.2%0.060.55Since 2014-01 0.00012014-01-062018-01-192.8%7.6%0.378.0%53.6%0.040.36 0.00052014-01-062018-01-193.2%7.7%0.428.2%54.2%0.040.39 0.0012014-01-062018-01-192.6%7.7%0.339.3%54.5%0.030.
13、28 0.0052014-01-062018-01-191.9%8.1%0.2310.8%54.5%0.020.17Source: J.P. Morgan Quantitative and Derivatives Strategy, BloombergFigure 30 shows the cumulated PnL of the VIX/VNKY strategy, fixed at a variance parameter of 0.0005. As expected, the strategy earns a stable and positive carry (in orange) v
14、ia the short VIX portion.Figure 30: Cumulated PnL in vol points (left) and long/short positions (right) of the VIX/VNKY strategy at a chosen variance parameter of 0.0005; the final PnL after costs is in blackSource: J.P. Morgan Quantitative and Derivatives Strategy, Bloomberg34Global Quantitative an
15、d (2) measurement equation connecting the observations with the state:?: State variable (which are unobserved)?: ObservationLet ?denote the information up to time t. Given the state space model, the state and the observations follow Gaussian distributions that evolve as below:1. Initialize state var
16、iable at time t = 0:?|?and ?|?are the filtered mean and variance of the state vector ?at time tAt time t = 0, we initialize the distribution of the state variable. For instance, take ?|?= 0 and ?|?= ?(10?) as a non-information prior with mean zero:?|?(?|?,?|?)2. Predict the state: Get the one-step-ahead prediction for the state variable at time t 0, given information up to t-1:?|?(?|?,?|?)From the state evolution
