An introduction to Taiwan market by using Markov model

1. An introduction to Taiwan market by using Markov model • models • examples • the kernel density estimation

2. 股票 價格 紅線:St 黑線:Xt ρ＋(x2) ρ＋(x1) ρ＋(x) ρ－(x1) ρ－(x) ρ－(x2) 第一天 收盤價 第二天 收盤價 第三天 收盤價

3. Markov model {Xn}

4. St ：表示沒有上下限的股票價格且它的 generator是

5. 股票價格 Xt 開盤價 x St 第一天收盤價

6. 股票價格 開盤價 x Xt St 第一天收盤價

7. 股票價格 開盤價 x St≡Xt 第一天收盤價

8. Examples • Binary model (Cox-Ross-Rubinstein)

9. Binary model • {Xn} is a martingale • If the state space of {Xn} is R+,then lim Xn =0. • If the state space of {Xn} is R,then {Xn} is recurrent.

10. European call

11. Example

12. European call

13. Optimal stopping time

14. Kernel density estimation

15. Positive recurrent Markov chain

16. Steps of the kernel density estimation • estimate q(x,y) such that pc(x,y)=q(x,y)dy • estimate Q+(x) such that pd(x,dy)=Q+(x)δρ+(dy) • estimate Q-(x) such that pd(x,dy)=Q-(x)δρ-(dy) • define estimators

17. Kernel density estimator

18. Another density estimator

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