Download presentation

Presentation is loading. Please wait.

Published byJohanna Fish Modified over 2 years ago

1
Introduction to Algorithmic Trading Strategies Lecture 2 Hidden Markov Trading Model Haksun Li haksun.li@numericalmethod.com www.numericalmethod.com

2
Outline Carry trade Momentum Valuation CAPM Markov chain Hidden Markov model 2

3
References Algorithmic Trading: Hidden Markov Models on Foreign Exchange Data. Patrik Idvall, Conny Jonsson. University essay from Linköpings universitet/Matematiska institutionen; Linköpings universitet/Matematiska institutionen. 2008. A tutorial on hidden Markov models and selected applications in speech recognition. Rabiner, L.R. Proceedings of the IEEE, vol 77 Issue 2, Feb 1989. 3

4
FX Market FX is the largest and most liquid of all financial markets – multiple trillions a day. FX is an OTC market, no central exchanges. The major players are: Central banks Investment and commercial banks Non-bank financial institutions Commercial companies Retails 4

5
Electronic Markets Reuters EBS (Electronic Broking Service) Currenex FXCM FXall Hotspot Lava FX 5

6
Fees Brokerage Transaction, e.g., bid-ask 6

7
Basic Strategies Carry trade Momentum Valuation 7

8
Carry Trade Capture the difference between the rates of two currencies. Borrow a currency with low interest rate. Buy another currency with higher interest rate. Take leverage, e.g., 10:1. Risk: FX exchange rate goes against the trade. Popular trades: JPY vs. USD, USD vs. AUD Worked until 2008. 8

9
Momentum FX tends to trend. Long when it goes up. Short when it goes down. Irrational traders Slow digestion of information among disparate participants 9

10
Purchasing Power Parity McDonald’s hamburger as a currency. The price of a burger in the USA = the price of a burger in Europe E.g., USD1.25/burger = EUR1/burger EURUSD = 1.25 10

11
FX Index Deutsche Bank Currency Return (DBCR) Index A combination of Carry trade Momentum Valuation 11

12
CAPM 12

13
Alpha 13

14
Bayes Theorem 14

15
Markov Chain s2: MEAN- REVERTIN G s1: UP s3: DOWN a22 = 0.2 a11 = 0.4a33 = 0.5 a12 = 0.2 a21 = 0.3 a23 = 0.5 a32 = 0.25 a13 = 0.4 a31 = 0.25 15

16
Example: State Probability 16

17
Markov Property 17

18
Hidden Markov Chain 18

19
Markov Chain s2: MEAN- REVERTIN G s1: UP s3: DOWN a22 = ? a11 = ?a33 = ? a12 = ? a21 = ? a23 = ? a32 = ? a13 = ? a31 = ? 19

20
Problems 20

21
Likelihood Solutions 21

22
Likelihood By Enumeration 22

23
Forward Procedure 23

24
Backward Procedure 24

25
Decoding Solutions 25

26
Decoding Solutions 26

27
Maximizing The Expected Number Of States 27

28
Viterbi Algorithm 28

29
Viterbi Algorithm 29

30
Learning Solutions 30

31
As A Maximization Problem 31

32
Baum-Welch 32

33
Xi 33

34
Estimation Equation 34

35
Estimation Procedure 35

36
Conditional Probabilities Our formulation so far assumes discrete conditional probabilities. The formulations that take other probability density functions are similar. But the computations are more complicated, and the solutions may not even be analytical, e.g., t-distribution. 36

37
Heavy Tail Distributions t-distribution Gaussian Mixture Model a weighted sum of Normal distributions 37

38
Trading Ideas Compute the next state. Compute the expected return. Long (short) when expected return > (<) 0. Long (short) when expected return > (<) c. c = the transaction costs Any other ideas? 38

39
Experiment Setup EURUSD daily prices from 2003 to 2006. 6 unknown factors. Λ is estimated on a rolling basis. Evaluations: Hypothesis testing Sharpe ratio VaR Max drawdown alpha 39

40
Best Discrete Case 40

41
Best Continuous Case 41

42
Results More data (the 6 factors) do not always help (esp. for the discrete case). Parameters unstable. 42

43
TODOs How can we improve the HMM model(s)? Ideas? 43

Similar presentations

OK

WHATIS FOREX MARKET? WHATIS. www.jrq.com WHAT IS FOREX? Forex stands for foreign exchange. it’s also referred as FX or currency market. This is a place.

WHATIS FOREX MARKET? WHATIS. www.jrq.com WHAT IS FOREX? Forex stands for foreign exchange. it’s also referred as FX or currency market. This is a place.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on types of forest in india Ppt on transportation in plants Ppt on media research jobs Ppt on total internal reflection occurs Ppt on satellite orbital slots Ppt on new zealand culture clothing View ppt on iphone Ppt on project proposal writing Ppt on online hotel booking Ppt on summary writing techniques