Fuzzy temporal meta-clustering of financial trading volatility patterns

Pawan Lingras; Farhana Haider; Matt Triff

doi:10.3934/bdia.2017018

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2018, Volume 0. Doi: 10.3934/bdia.2017018

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Fuzzy temporal meta-clustering of financial trading volatility patterns

Department of Mathematics & Computing Science, Saint Mary's University, Halifax, Nova Scotia, B3H3C3, Canada

Corresponding author:Pawan Lingras and Matt Triff
Corresponding author:Pawan Lingras and Matt Triff;
Corresponding author:Pawan Lingras and Matt Triff

Received: June 30, 2017

Revised: February 28, 2018

Early access: March 2018

Abstract Full Text(HTML) Figure(14) / Table(10) Related Papers Cited by

Abstract

A volatile trading pattern on a given day in a financial market presents an opportunity for traders to maximize the difference between their buying and selling prices. In order to formulate trading strategies it may be advantageous to study typical trading patterns. This paper first describes how clustering can be used to profile typical volatile trading patterns. Fuzzy c-means provides a better description of individual trading patterns, since they can display certain aspects of different trading profiles. While daily volatility profile is a useful indicator for trading a stock, the volatility history is also an important part of the decision making process. This paper further proposes a fuzzy temporal meta-clustering algorithm that not only captures the daily volatility but also puts it in a historical perspective by including the volatility of previous two weeks in the meta-profile.

Keywords:

Mathematics Subject Classification: Primary: 91C20, 62-07; Secondary: 91B84.

Citation:

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Figure 1. Cluster Scatter

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Figure 2. DB Index

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Figure 3. Centroids of 5 Clusters after Ranking

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Figure 4. Average Chronological Daily Patterns

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Figure 5. Fuzzy Centroids of 5 Clusters after Ranking

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Figure 6. Flowchart of Recursive Meta-clustering

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Figure 7. Fuzzy Temporal Meta-clustering Algorithm

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Figure 8. Ranks in Final Temporal Cluster

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Figure 9. Ranks of day 2012-01-12 and last 10 days of Instrument Z_2

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Figure 10. Ranks of day 2011-10-03 and last 10 days of Instrument 3_1

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Figure 11. Ranks of day 2011-12-16 and last 10 days of Instrument A_10

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Figure 12. Ranks of day 2011-08-16 and last 10 days of Instrument 3_1

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Figure 13. Ranks of day 2012-01-04 and last 10 days of Instrument A_10

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Figure 14. Ranks of day 2011-11-01 and last 10 days of Instrument A_113

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Table 1. Calculation of Percentiles for a Sample Record

Percentile	10%	25%	50%	75%	90%
Percentile of avgp (avgpPerc)	0.9841346	0.9873798	0.9927885	0.9951923	0.9966346

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Table 2. Crisp Cluster Cardinalities

Cluster number	1	2	3	4	5
Percentile values	14125	8676	3349	817	45
Black Scholes	14182	8990	3061	684	95

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Table 3. Cluster Intersections

	cdvr1	cdvr2	cdvr3	cdvr4	cdvr5
cpr1	10430	3104	519	67	5
cpr2	3411	4047	1089	123	6
cpr3	339	1727	1047	223	13
cpr4	2	112	404	258	41
cpr5	0	0	2	13	30

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Table 4. Fuzzy memberships for different stocks

Day:Instrument	fcpr_i	fcpr₂	fcpr₃	fcpr₄	fcpr₅	Avg Rank
2011-08-16:3_1	0.04	0.06	0.09	0.35	0.46	4.14
2011-08-17:3_1	0.85	0.13	0.03	0	0	1.19
:
2012-01-31:3_1	0.06	0.16	0.65	0.12	0.01	2.86
:
2011-08-16:Z_2	0.97	0.03	0.01	0	0	1.04
:
2012-01-31:Z_2	0.93	0.05	0.01	0	0	1.09

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Table 5. Static Part of Percentile Data

Day:Instrument	p10	p25	p50	p75	p90
2011-08-16:3_1	0	0.28	0.56	0.67	0.78
2011-08-17:3_1	0	0	0.04	0.09	0.11
:
2012-01-31:3_1	0	0	0.15	0.29	0.46
:
2011-08-16:Z_2	0	0.027	0.045	0.05	0.05
:
2012-01-31:Z_2	0	0.01	0.019	0.03	0.11

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Table 6. Ranked Clusters for Percentile Data after first iteration

		Centers
Rank	Cluster	p10	p25	p50	p75	p90
1	C2	0	0.02	0.03	0.06	0.08
2	C5	0	0.05	0.10	0.16	0.21
3	C4	0	0.09	0.19	0.28	0.35
4	C1	0	0.16	0.35	0.48	0.57
5	C3	0	0.30	0.66	0.88	1.00

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Table 7. Dynamic Part after first iteration

Day_m+1:Instrument	d_m-9	d_m-8	d_m-7	d_m-6	d_m-5	d_m-4	d_m-3	d_m-2	d_m-1	d_m
2011-08-16:3_1	2.69	2.69	2.70	2.70	2.69	2.70	2.68	2.70	2.70	2.69
2011-08-17:3_1	2.69	2.70	2.70	2.69	2.70	2.68	2.70	2.70	2.69	4.14
:
2012-01-31:3_1	1.07	2.10	3.78	1.25	1.81	3.58	4.06	1.09	1.42	3.56
:
2011-08-16:Z_2	2.69	2.70	2.70	2.70	2.70	2.70	2.70	2.70	2.70	2.69
:
2012-01-31:Z_2	1.09	2.90	2.89	1.15	3.04	1.87	2.00	3.01	2.05	1.71

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Table 8. Concatenated Static Part(SP) and Dynamic Part(DP) after first iteration

	SP					DP
Day:Instrument	p10	p25	p50	p75	p90	d_m-9	d_m-8	d_m-7	d_m-6	d_m-5	d_m-4	d_m-3	d_m-2	d_m-1	d_m
2011-08-16:3_1	0	0.28	0.56	0.67	0.78	2.69	2.69	2.70	2.70	2.69	2.70	2.68	2.70	2.70	2.70
2011-08-17:3_1	0	0	0.04	0.09	0.11	2.69	2.70	2.70	2.69	2.70	2.68	2.70	2.70	2.69	4.14
:
2012-01-31:3_1	0	0	0.15	0.29	0.46	1.07	2.10	3.78	1.25	1.81	3.58	4.06	1.09	1.42	3.56
:
2011-08-16:Z_2	0	0.03	0.045	0.05	0.05	2.69	2.70	2.70	2.70	2.70	2.70	2.70	2.70	2.70	2.69
:
2012-01-31:Z_2	0	0.01	0.02	0.03	0.11	1.09	2.90	2.89	1.15	3.04	1.87	2.00	3.01	2.05	1.71

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Table 9. Cluster Centers after clustering with Concatenated Profile

		SP					DP
Rank Cluster		p10	p25	p50	p75	p90	d_m-9	d_m-8	d_m-7	d_m-6	d_m-5	d_m-4	d_m-3	d_m-2	d_m-1	d_m
1	C5	0	0.0530	0.1123	0.1720	0.2227	1.9925	1.9849	1.9812	1.9698	1.9645	1.9569	1.9539	1.9481	1.9409	1.9376
2	C2	0	0.0531	0.1124	0.1721	0.2227	1.9933	1.9857	1.9820	1.9706	1.9653	1.9576	1.9546	1.9488	1.9415	1.9382
3	C4	0	0.0531	0.1124	0.1721	0.2228	1.9937	1.9861	1.9824	1.9710	1.9657	1.9581	1.9550	1.9492	1.9419	1.9386
4	C1	0	0.0531	0.1124	0.1722	0.2229	1.9943	1.9867	1.9830	1.9716	1.9663	1.9587	1.9556	1.9498	1.9424	1.9391
5	C3	0	0.0532	0.1124	0.1722	0.2229	1.9946	1.9871	1.9834	1.9720	1.9666	1.9590	1.9501	1.9427	1.9559	1.9393

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Table 10. Final Ranked Centers for Percentile Data

Rank Cluster		p10	p25	p50	p75	p90	d_m-9	d_m-8	d_m-7	d_m-6	d_m-5	d_m-4	d_m-3	d_m-2	d_m-1	d_m
1	C2	0	0.04	0.08	0.12	0.15	1.20	1.17	1.14	1.12	1.11	1.10	1.10	1.11	1.13	1.15
2	C4	0	0.05	0.10	0.15	0.19	2.24	2.20	2.16	2.14	2.11	2.10	2.10	2.11	2.12	2.14
3	C3	0	0.05	0.10	0.16	0.21	3.04	3.03	3.03	3.03	3.02	3.02	3.02	3.02	3.03	3.03
4	C1	0	0.05	0.11	0.17	0.22	3.82	3.86	3.89	3.92	3.94	3.95	3.97	3.98	3.99	3.99
5	C5	0	0.07	0.14	0.21	0.27	4.70	4.75	4.78	4.81	4.83	4.84	4.83	4.82	4.79	4.76

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