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| 研究生： |
林義評 Lin, Yi-Ping |
|---|---|
| 論文名稱： |
應用神經網路於金融交換與Black-Scholes定價模式之探討與其意義分析 A study and analysis of applying neural networks to the financial swapa and the Black-Scholes pricing model |
| 指導教授： |
蔡瑞煌
Tsai, Rai-Hwan |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 資訊管理學系 Department of Management Information System |
| 論文出版年： | 1998 |
| 畢業學年度： | 86 |
| 語文別： | 英文 |
| 論文頁數： | 81 |
| 中文關鍵詞： | 倒傳遞網路 、裡解神經網路 、Black-Scholes 定價模式 、金融交換 、敏感度分析 、滯留區分析 |
| 外文關鍵詞： | BP, RN, Black-Scholes pricing model, Financial swaps, Sensitivity analysis, Dead region analysis |
| 相關次數： | 點閱：123 下載：0 |
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本篇論文旨在分析神經網路學習績效，並提出一套學習演算法，結合倒傳遞網路(BP)與理解神經網路(RN)，命名為RNBP，這套學習演算法將與傳統的BP做比較，以兩個不同的財務金融領域的應用，一個是選擇權上Black-Scholes訂價模式的模擬，一個是金融交換上利率的預測。主要績效的評估準則是以學習的效率與模擬、預測的準確度為依據。
此外，本論文的另一個重點是提出一套對於神經網路系統進一步分析的方法與工具，敏感度分析(Sensitivity Analysis)與滯留區(Dead Region)分析，藉以瞭解神經網路系統是否具有效地良好學習或被一般化的能力，從神經網路的角度來說，這也是BP與RNBP的另一個績效比較標準。本研究的結果顯示RNBP在預測準確度上較BP為優良，但是在學習效率與預測能力的穩定性上並沒有呈現一致性的結論；此外，敏感度分析與滯留區分析的結果也幫助神經網路在應用領域上有更深入的瞭解。
在過去，神經網路的應用者往往忽略了進一步瞭解神經網路的重要性與可行性，本論文的貢獻在於藉由分析神經網路所學習的知識，幫助應用者進一步瞭解神經網路表達的訊息在應用領域上所隱含的實質意義。
The study attempts to analyze the learning performance of neural networks in applications, and propose a new learning procedure for the layered feedforward neural network systems, named KNBP, which binds RN and BP learning algorithms. Two artificial neural networks, BP and KNBP, here are both applied to two financial fields, the simulation of Black-Scholes pricing model for the call options and the midrates forecasting in financial swaps. The explicit performance comparison between the two artificial neural network systems is mainly based on two criteria, which are learning efficiency and forecasting effectiveness.
Then we propound a mathematical methodology of sensitivity analysis and the dead regions to deeply explore inside the network structures to see whether the models of ANNS are actually well trained or valid, and thus setup an alternative comparable criterion. The results from this study show that RNBP performs better than BP in forecasting effectiveness, but RNBP obtains neither a consistent learning efficiency in cases nor a stable forecasting ability. Furthermore, the sensitivity analysis and the dead region analysis provide a deeper view of the ANNs in the applied fields.
In the past, most studies applying neural networks ignored the importance that it is feasible and advantageous to obtain more useful information via analyzing neural networks. The purpose of the research is to help further understanding to the information discovery resulted from neural networks in practical applications.
CHAPTER 1 INTRODUCTION-----1
CHAPTER 2 LITERATURE REVIEW-----3
2.1. BACK PROPAGATION NEURAL NETWORKS-----4
2.2. REASONING NEURAL NETWORKS-----7
2.3. KNBP-AN ALTERNATIVE LEARNING PROCEDURE-----11
2.4. APPLICATIONS OF ANNS TO THE FINANCIAL FIELDS-----12
2.5. THE OPTION-----14
2.5.1. Black-Scholes pricing model-----14
2.5.2. Partial derivatives of Black-Scholes formula-----15
2.6. THE SWAP-----16
2.6.1. What is swap - definition-----16
2.6.2. Derivation of swap midrates from Eurodollar futures-----18
2.7. SENSITIVITY ANALYSIS WITHNEURAL NETWORKS-----20
2.8. A MODIFIED METHODOLOGY OF SENSITIVITY ANALYSIS-----24
2.9. THE DEAD REGION-----28
CHAPTER 3 EXPERIMENT DESIGNS AND METHODOLOGY-----30
3.1. EXPERIMENT DESIGNS AND PERFORMANCE CRITERIA-----30
3.2. THE PRICING MODEL OF CALL OPTIONS-----32
3.3. THE FORECASTING OF SWAP MIDRATES-----35
3.3.1. Moving forecasting-----35
3.3.2. Checking the data-----39
CHAPTER 4 PERFORMANCE AND ANALYSIS-----41
4.1. SIMULATION PERFORMANCE OF BP AND RNBP IN BLACK-SCHOLES FORMULA-----41
4.1.1. Simulation performance-----41
4.1.2. Sensitivity analysis-----47
4.1.3. The dead region analysis-----51
4.2. FORECASTING RESULTS OF BP AND RNBP IN SWAP MIDRATES-----54
4.2.1. Forecast performance-----54
4.2.2. A further discussion of RNBP-----59
4.2.3. Summary in swap rates forecasting-----63
4.2.4. Sensitivity analysis-----64
CHAPTER 5 SUMMARY-----67
5.1. DISCUSSIONS FROM THE SIMULATIONS AND FORECASTS-----67
5.3. CONTRIBUTIONS AND FUTURE WORK-----68
REFERENCE-----70
APPENDIX A-----74
APPENDIX B-----75
APPENDIX C-----78
Figure Index
FIGURE 2.1. MULTI-LAYERED PECEPTRON NETWORK STRUCTURE-----4
FIGURE 2.2. THE SOFTEN LEARNING PROCEDURE-----8
FIGURE 2.3. RNBP LEARNING PROCEDURE-----11
FIGURE 2.4. THE GENERIC SWAP STRUCTURE-----18
FIGURE 2.5. THE SENSITIVITY CURVE-----26
FIGURE 3.1. IN-THE-MONEY CALLPRICES INTRAINING PATTERNS-----34
FIGURE 3.2. OUT-OF-THE-MONEY CALLPRICES IN TRAINING PATTERNS-----34
FIGURE 3.3. SWAP MIDRATES FROM AUGUST 1993 TO MAY 1994-----36
FIGURE 3.4. THE METHOD OF MOVING SIMULATION-----38
FIGURE 3.5. THE FORECASTING RESULTS OF APPLYING AR(5) MODEL TO THE DATA OF E<sub>1</sub> AND E<sub>3</sub>-----40
FIGURE 4.1. CONVERGING ERRORS IN EARLY LEARNING ITERATIONS-----45
FIGURE 4.2. (A),(B),(C),(D) AND (E) SENSITIVITY VALUES OF THE FIVE VARIABLES-----50
FIGURE 4.3. FREQUENCY DISTRIBUTION IN IN-THE-MONEY SIMULATIONS-----52
FIGURE 4.4. FREQUENCY DISTRIBUTION IN IN-THE-MONEY SIMULATIONS-----52
FIGURE 4.5. THE FORECASTING RESULTS OF BP AND RNBP IN E<sub>1</sub>-----54
FIGURE 4.6. THE FORECASTING RESULTS OF BP AND KNBP IN E<sub>2</sub>-----55
FIGURE 4.7. THE FORECASTING RESULTS OF BP AND KNBP IN E<sub>3</sub>-----55
FIGURE 4.8. THE SUMMARY OF THE AMOUNTS OF HIDDEN NODES RECRUITED DURING THE LEARNING PROCESSES OF RN IN E<sub>3</sub>. THE LAST DATA POINT ON EACH LINE CORRESPONDS TO THEAMOUNT OF HIDDEN NODES RECRUITED AFTER THE PROCESSING OF THE LAST REASONING MECHANISM (REFERS TO FIGURE 2.2)-----61
FIGURE 4.9. AVERAGE SENSITIVITIES IN E<sub>1</sub>, E<sub>2</sub> AND E<sub>3</sub> RESULTED FROM BP AND RNBP-----66
Table Index
TABLE 2.1. THE DEFINITION OF THE USED NOTATIONS-----4
TABLE 2.2. BP'S LEASNING ALGORITHM-----7
TABLE 3.1. TRAINING DATA Of RN-----32
TABLE 3.2. RANGES OF INPUT VARIABLES OF TRAINING NETWORKS-----34
TABLE 3.3. SUMMARY OF THE FORECASTING BYAR(5) MODEL IN E<sub>1</sub> AND E<sub>3</sub>-----40
TABLE 4.1. IN-THE-MONEY SIMULATION RESULTS OF BP AND RNBP-----42
TABLE 4.2. OUT-OF-THE-MONEY SIMULATION RESULTS OF BP AND RNBP-----43
TABLE 4.3. STOPPING CRITERION WITH ERROR LEVEL = 0.02 (IN-THE-MONEY)-----45
TABLE 4.4. STOPPING CRITERION WITH ERROR LEVEL = 0.02 (OUT-OF-THE-MONEY)-----45
TABLE 4.5. THE DIFFERENCES OF SIMULATION DESIGNS FORM OTHER PREVIOUS STUDIES-----47
TABLE 4.6. SENSITIVITY ANALYSIS (IN-THE-MONEY)-----48
TABLE 4.7. SENSITIVITY AMALYSIS (OUT-OF-THE-MONEY)-----49
TABLE 4.8. SUMMARY OF THE FORECASTING BY BP AMD RNBP IN E<sub>1</sub>-----57
TABLE 4.9. SUMMARY OF THE FORECASTING BY BP AND RNBP IN E<sub>2</sub>-----57
TABLE 4.10. SUMMARY OF THE FORECASTING BY BP AND RNBP IN E<sub>3</sub>-----57
TABLE 4.11. THE SUMMARY OF THE EFFECTIVENESS-----58
TABLE 4.12. THE SUMMARY OF THE EFFICIENCY (TDENOTES THE AMOUNT OF LEARNING ITERATIONS)-----59
TABLE 4.13. A FURTHER ANALYSIS OF THE SIMULATIONS WITH KNBP. N IS THE AMOUNT OF RECRUITED HIDDEN NODES. F DISPLAYS THE FREQUENCY OF OCCURRENCES. T REPRESENTS THE (AVERAGE) AMOUNT OF THE LEARNING ITERATIONS. R IS THE MEAN RELATIVE ERROR. C DISPLAYS THE RATE OF PREDICTING CORRECTLY THE DIRECTION OF CHANCE. SUBSCRIPT I DENOTES THE SIMULATION OF E<sub>1</sub>-----62
TABLE 4.14. THE CORRECT HIT RATE OF BP AND RNBP-----63
TABLE 4.15. SENSITIVITY ANALYSIS IN SWAP MIDRATES FORECASTING-----65
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