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The profitability of a trading system based on the momentum-like effects of price jumps was tested on the time series of 7 assets (EUR/USD, GBP/USD, USD/CHF and USD/JPY exchange rates and Light Crude Oil, E-Mini S&P 500 and VIX Futures), in each case for 7 different frequencies (ranging from 1-Minute to 1-Day), over a period of more than 20 years (for all assets except for the VIX) ending in the second half of 2015. The proposed trading system entered long and short trades in the direction of price jumps, for the closing price of the period in which the jump occurred. The position was held for a fixed number of periods that was optimized on the in-sample period. Jumps were identified with the non-parametric L-Estimator whose inputs (period used for local volatility calculation and confidence level used for jump detection) were also optimized on the in-sample period. The proposed system achieved promising results for the 4 currency markets, especially at the 15-minute and 30-minute frequencies at which 3 out of the 4 tested currencies turned profitable (with highest profits achieved by USD/CHF, followed by EUR/USD and GBP/USD), with the profits totaling up to 30-50% p.a. in the case of a high-leverage scenario, or 15-25% in the case of a low-leverage scenario. Additionally, the 5-minute frequency turned profitable for USD/CHF and the 4-hour frequency for GBP/USD, while the 1-minute frequency was unprofitable in all cases due to the commissions and the 1-day frequency contained too few jumps to make any conclusions. As for the futures markets, the system achieved profits only on the Light Crude Oil market, on the frequencies of 1-hour, 4-hour and 1-day, with the profits totaling up to 20% p.a. in the case of high leverage or 10% p.a. in the case of low leverage. For USD/JPY, E-Mini S&P 500 Futures and VIX Futures the system achieved mostly a loss. We attribute this (in the latter two cases) to the effect of a rising market risk premium in the case of negative jumps, going against the jump-momentum effect used by the system.
Non-parametric approach to financial time series jump estimation, using the L-Estimator, is compared with the parametric approach utilizing a Stochastic-Volatility-Jump-Diffusion (SVJD) model, estimated with MCMC and extended with Particle Filters to estimate the out-sample evolution of its latent state variables, such as the jump occurrences. The comparison is performed on simulated time series with different kinds of dynamics, including Poisson jumps, self-exciting Hawkes jumps with long-term clustering, as well as co-jumps. In addition to that, a comparison is performed on the real world daily time series of 4 major currency exchange rates. The results from the simulation study show that for the purposes of in-sample estimation does the MCMC based parametric approach significantly outperform the L-Estimator. In the case of the out-sample estimates, based on a combination of MCMC an Particle Filters, used to sequentially estimate the jump occurrences immediately at the times at which the jumps occur, does the parametric approach achieve a similar accuracy as the non-parametric one in the case of the simulations with Poisson jumps that are relatively large, and it outperforms the non-parametric approach in the case of Hawkes jumps when the jumps are large. On the other hand, the L-Estimator provides better results than the parametric approach in all of the cases when the simulated jumps are small (1% or less), regardless of the jump process dynamics. The application of the methods to foreign exchange rate time series further shows that the estimates of the parametric method may be biased in the case when large outlier jumps occur in the time series as well as when the stochastic volatility grows too high (as happened during the crisis). In both of these cases, the non-parametric L-Estimator based approach seems to provide more robust jump estimates, less influenced by the mentioned issues.