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Calibrating L-A Model to Chinese Stocks

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  1. Calibrating L-A Model to Chinese Stocks Chun Chen Sharalyn Chen Fei Lin Hechen Yu

  2. Agenda • Background & motivations • Model & calibration algorithm • Sensitivity of parameters • Calibration Results • Volkswagen • Air China • China Rail Construction • Conclusions

  3. Background • Project based on Avellaneda and Lipkin’s paper “A Dynamic Model for Hard-to-Borrow Stocks” • Definitions: • Short selling • Hard-to-borrow stocks (HTB): insufficient float available for lending • Buy–ins: forcibly repurchase to cover short positions • Phenomena associated with HTBs • Artificially high prices and sharp drops due to buy-ins • Examples, Volkswagen October 2008

  4. A classic HTB example: Volkswagen

  5. Motivation • 61 stocks listed on both Hong Kong (H shares) and Shanghai (A shares) stock exchanges • 51 out of 61 can be shorted in HK • None can be shorted in Shanghai • Same stock, but different price movements. • Can the price differentials be explained by the varying degree of hard-to-borrowness?

  6. Model • St: stock price at time t • λt: buy-in rate • dNλt: Poisson process with intensity λ over (t, t+dt) • σ and κ : respective volatilities • ϒ: price elasticity of demand due to buy-ins • α: speed of mean reversion • X bar: long term equilibrium of Xt • β: impact of stock price change on buy-in intensity

  7. Calibration Algorithm • 6 dimensional optimization problem • Minimize objective function • max|pdfdata(r) – pdffitted(r)| • Sum of differences in mean + variance + skewness + kurtosis • Grid Search to identify good initial values • Then use Matlabfmincon for local optimization

  8. FittingSensitivity of parameters: σ

  9. FittingSensitivity of parameters : σ • 1. σ

  10. FittingSensitivity of parameters: ϒ

  11. FittingSensitivity of parameters: ϒ • 2. γ

  12. FittingSensitivity of parameters: Xbar, α, β, κ

  13. Calibration Results - VOW • Sample period: 1/1/2008 – 12/31/2008

  14. Fitting • Imperfect fit due to: • Fat tail returns of the actual stocks vs. Gaussian assumptions • Model nature as below Sudden drop Gradual drift

  15. Calibrating Chinese Stocks • In general, Chinese stock exhibit bubble effects with A share price exceeding H share price • But this bubble effects are likely due to systematic factors • Calibration divide into two categories: • 1: Sample period including bubbles (Air China) • 2: Sample period without bubbles (Air Railway Con)

  16. Calibration Category 1Sample period with bubbles (Air China)

  17. Calibration Results – Air China • Sample period: 08/18/2006 – 04/19/2010 • Fitted parameters: • Calibration shows that σ, ϒ, α and X bar are significantly different between SH and HK • σ: due to differences in actual volatilities • ϒ: due to differences in price ranges during sample period • X bar: reveals that “buy-in” intensity is higher for SH • α: reveals that the range of “buy-in” intensity fluctuation is higher in SH

  18. Calibration Results – Air China • Generally good fit except A share kurtosis Fitted kurtosis without extreme left tail points = 2.8653

  19. Calibration Category 2Sample period without bubbles (China Railway Construction)

  20. Calibration Results – China Rail Con • Sample period: 3/13/2008 – 4/19/2010 • Fitted parameters: • Calibration shows that σ, κ, α and β are significantly different between SH and HK • σ: due to differences in actual volatilities • ϒ: no difference as price ranges are similar • κ, α and β: hard to detect individual impacts, but can be interpreted together

  21. Calibration Results – China Rail Con • The net effect of κ, α and β is on the movement of “buy-in” intensity λ • λ varies between 0 and 40 for both A share and H share A share H share

  22. Calibration Results – China Rail Con • Both parameter sets fit data well • ϒ =0.015 very small for both stocks A Share H Share

  23. Conclusions • Calibration including period of bubbles (Air China) • Calibrated L-A model have significant ϒ value, suggesting its ability to capture bubble effects, although such bubble is most likely due to systematic factors rather than HTB dynamics • Calibration excluding period of bubbles (China Rail Con) • Calibrated L-A model have very small ϒ value • Calibration could have multiple optimal parameters. It is essential to use multiple objective functions and criteria

  24. Thank you! Questions?