Æ?èµ10384 ÆÒµ27720120153852 aò? UDC Æ Æ Ø žc9d/5aé7k½ )ºÚý ÿ The Interpretability and Predictability of Time-varying and Contagious Jumps to the Financial Markets H r 6 µ ö[œ!!ë Ö ; µ 7 K Æ Ø JFϵ Ø Fžmµ Æ ÇƒFϵ 2 0 1 6 c 5 2 0 1 6 c 5 2 0 1 6 c 5 F ÌRµ µ <µ 2016 c 5
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Abstract This study explores the interpretability and predictability of time-varying and contagious jumps to the financial markets. We theoretically and empirically investigate whether jumps can predict conditional market returns and volatilities, whether jumps can help to explain the exchange rate puzzles and to study the exchange rate predictability, and how the jumps affect traders behavior in the high-frequency trading future and option markets. We change the constant jump intensity as in the LPW and Du models with time-varying intensity following an autoregressive conditional jump intensity (ARJI) process and a squared bessel (SB) process, and apply calibrated jump premiums to predict excess market returns and volatilities. We show that all calibrated jump premiums have significant predictive power in sample and out-of-sample. We find that in the U.S. market LPW s model forecasts excess returns and volatilities better. The ARJI process of jump intensity predicts excess returns better, and SB process forecasts volatilities better. In the Australian market we find that, the model with ARJI process of jump intensity predicts Australian market returns and volatilities better. LPW s model predicts future market returns better and Du s model performs better for volatilities. In the Chinese market, Du s model forecasts excess returns and volatilities better and the model with SB process of jump intensity performs better in predicting the dynamics. This study supplies new evidence regarding the predictive power of jumps. Then, we extends a single currency long-run risk model with time-varying jumps to a multi-currency model, and applies it to the U.S. and the U.K. markets to analyze the interpret ability and forecast power of time-varying jumps to the FX market. We find that the model with jumps matches the equity and exchange rate dynamics very well and performs better in explaining and forecasting the exchange rate dynamics, than the classical long-run risk model without jumps. Results from this study shed new light on three exchange rate puzzles, namely, the international equity premium puzzle, the forward premium puzzle, and the exchange rate disconnect puzzle. The model is also economically important in predicting the exchange rate growth. After that, we study the predict ability of contagious jumps to the high-frequency trading future and option markets and check how exogenous jumps affect traders order behavior. We employ the classical self-exciting Hawkes point processes to model the dynamics and interaction of the order arrivals of the high-frequency trading S&P 500 Index futures and options in the U.S. market. We investigate the impact of a big overnight jump on the arrival times of orders by using the change of the branching III
ratios to measure whether there exist significant structure changes of contagion behavior after a big exogenous overnight jump occurs. We analyze all of the limit orders, market orders and cancelations in the ask and bid sides, and find that the order arrivals in both of the future and the option markets have significant structure changes after a big overnight jump. We also find that traders have different responses when facing negative-jump and positive-jump cases, and that there are little mutual-excitation evidence of the futures on the options in comparison to the strong self-excitation of the options itself. At last, we briefly discussing the implication of our study to the Chinese market. Key Words: Time-varying jump intensity, Return predictability, Volatility predictability, Exchange rate puzzles, Contagious jumps. IV
8 ¹ Á... I Abstract... III L 8¹... XIV ã8¹... XV 1 Ù XØ... 1 1.1 ïäµú znã.................................................. 2 1.2 ïäg.............................................................. 6 1.3 (ØÚuy....................................................... 9 1.4 Ù(.............................................................. 11 1Ù žcaädýÿuåµäu ½ yâ... 13 2.1 Úó................................................................... 13 2.2.................................................................... 16 2.2.1 ü Ä:...................................................... 16 2.2.2 ü ÅL..................................................... 18 2.3 O................................................................... 19 2.3.1 êâ............................................................... 19 2.3.2 O {.......................................................... 20 V
2.3.3 ëê½.......................................................... 21 2.4 êš(j Û......................................................... 21 2.4.1 O(J.......................................................... 21 2.4.2 =žaädé ÂÃÚÅÄÇ 8.................... 25 2.4.3 áï aädé ÂÃýÿ........................... 27 2.4.4 áï aädéåäçýÿ.................................. 28 2.4.5 áï(j)º................................................... 29 2.4.6 u........................................................ 31 2.4.7 Ï aädýÿuå....................................... 32 2.5 e³yâ............................................................ 34 2.5.1 áï aädée³½ ÂÃýÿ........................... 34 2.5.2 áï aädée³ yåäç 8...................... 35 2.5.3 e³½ Ï aädýÿuå............................. 36 2.6 Iyâ............................................................ 40 2.6.1 ëêo.......................................................... 40 2.6.2 áï aädé I½ ÂÃýÿ........................... 42 2.6.3 áï aädé I½ yåäçýÿ................. 43 2.6.4 I½ Ï aädýÿuå............................. 49 2.7 Ù(.............................................................. 52 1nÙ aºx! ÇCz9 ½ ƒ... 53 3.1 Úó................................................................... 53 VI
3.2.................................................................... 56 3.2.1.Ä.......................................................... 56 3.2.2.).......................................................... 58 3.3 êâ................................................................... 60 3.3.1 ëêz............................................................ 60 3.4 êš(j.............................................................. 62 3.4.1 O............................................................... 62 3.4.2 O {.......................................................... 62 3.4.3.(JV.S. ý êâ............................................ 65 3.4.4 )û ƒ nø Û......................................... 71 3.4.5 )º ½ ă............................................ 73 3.5 Ù(.............................................................. 82 1oÙ D/5a pªïà9ï½ 1... 85 4.1 Úó................................................................... 85 4.2 Hawkes L.......................................................... 90 4.2.1 ücþœ¹........................................................ 90 4.2.2 VCþœ¹........................................................ 92 4.3 êâú {............................................................ 94 4.3.1 êâ............................................................... 94 4.3.2 êâ a.......................................................... 95 4.3.3 {............................................................... 96 VII
4.4 (J................................................................... 99 4.4.1 ücþœ¹........................................................ 99 4.4.2 wí5u........................................................ 110 4.4.3 êïàúïvcþ(j.................................... 112 4.5 (................................................................... 120 1ÊÙ é I½ / Ú Â... 121 18Ù (Ø... 125 6.1 ïä(ø.............................................................. 125 6.2 Øv Ð"............................................................ 126 N¹µ aïºx.)... 129 ë z... 131 ôöæ Æ ÏmïÄ J... 143... 145 VIII
Table of Contents Abstract (In Chinese) I Abstract (In English) Tables Figures V XIV Chapter 1 Introduction 1 1.1 Background and literature reviews.................. 2 1.2 Research strategy............................ 6 1.3 Main results and research Innovation................. 9 1.4 Structural arrangement........................ 11 Chapter 2 Predictability of Time-varying Jump Premiums: Evidence Based on Stock Markets 13 2.1 Introduction............................... 13 2.2 The model................................ 16 2.2.1 Two basic models......................... 16 2.2.2 Two stochastic processes..................... 18 2.3 Calibration................................ 19 2.3.1 Data................................ 19 2.3.2 Calibration methodology..................... 20 2.3.3 Parameter settings........................ 21 2.4 Analysis of numerical results...................... 21 2.4.1 Calibration results........................ 21 2.4.2 Regressions of excess stock returns and volatilities on contemporaneous jump premiums.................... 25 2.4.3 Forecasting excess stock returns with jump premiums in the short run............................. 27 IX XV
2.4.4 Forecasting volatilities with jump premiums in the short run.. 28 2.4.5 Interpretation of results in the short run............. 29 2.4.6 Out-of-sample test........................ 31 2.4.7 Predictive power of the jump premium in the long run..... 32 2.5 Australian evidence........................... 34 2.5.1 Forecasting Australian market returns with jump premiums in the short run........................... 34 2.5.2 Regression of Australian realized volatilities on jump premiums in the short run....................... 35 2.5.3 Predictive power of the jump premium in the long run for Australian market........................... 36 2.6 Chinese Evidence............................ 40 2.6.1 Parameter Calibration...................... 40 2.6.2 Forecasting Chinese market returns with jump premiums in the short run............................. 42 2.6.3 Regression of Chinese realized volatilities on jump premiums in the short run.......................... 43 2.6.4 Predictive power of the jump premium in the long run for Chinese market............................ 49 2.7 Concluding Remarks.......................... 52 Chapter 3 Jump Risks, Exchange Rate Changes, and the FX Markets Puzzles 53 3.1 Introduction............................... 53 3.2 The model................................ 56 3.2.1 Model dynamics......................... 56 3.2.2 Model solution.......................... 58 3.3 Data.................................... 60 3.3.1 Parameterization......................... 60 3.4 Numerical results............................ 62 3.4.1 Calibration............................ 62 3.4.2 Calibration methodology..................... 62 X
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