文斯最佳出價比例在選擇權價差組合交易盈利之研究

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姚志鴻(Chih-Hong Yao) 查詢紙本館藏

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財務金融學系在職專班

論文名稱

文斯最佳出價比例在選擇權價差組合交易盈利之研究
(Study on the Profitability of Option Spread Trading Using Vince′s Optimal Bidding Fraction)

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摘要(中)

資金管理是金融交易中最重要的問題之一。許多資金管理技巧基於凱利準則，這是一種理論優化方法，可用於確定持有部位大小的最佳比例。對於資金管理，理論和實際交易之間仍存在很大差距。我們使用一種基於凱利準則的選擇權交易策略。儘管選擇權的價格波動性很高，但可以通過在不同履約價上進行多頭或空頭操作，形成各種選擇權價差組合，以預先鎖定損失和利潤。
本研究期間為2013年1月4日至2023年2月22日，通過持有選擇權價差組合交易，我們可以獲得固定的利潤和損失分布。我們使用了一種選擇權交易方法，通過文斯最佳出價比例的演算法，計算最佳出價比例，找到有利可圖的選擇權組合。我們使用的模型是一種判斷選擇權價差組合是否為有利可圖的方法，同時具有持有部位大小的資金管理。實驗表明，我們的方法在實際場景中是可行的。當投資者已經找到可盈利的投資組合時，還要注意資金控管的部分當出價比例過高時，不只無法得到預期的正報酬，反而出現虧損的結果。最後一部分提供了未來的工作方向。

摘要(英)

Money management is one of the most important issues in financial trading. Many money management techniques are based on the Kelly criterion, which is a theoretical optimization method used to determine the optimal proportion of position size. However, there is still a significant gap between theory and practical trading when it comes to money management. We employ an options trading strategy based on the Kelly criterion. Despite the high price volatility of options, various options spread combinations can be created by taking long or short positions at different strike prices to predefine both losses and profits.
The research period for this study spans from January 4, 2013, to February 22, 2023. By engaging in options spread combination trades, we can achieve fixed profit and loss distributions.
We utilize an options trading approach that involves employing the algorithm of Vince′s Optimal fraction method to calculate the optimal bid ratios and identify profitable combinations of options. The model we use serves as a method for determining the profitability of options spread combinations while incorporating capital management in terms of position sizing. The experiments have shown that our method is feasible in practical scenarios. However, when investors have identified profitable investment portfolios, it is crucial to pay attention to the aspect of money management. If the bidding ratio is too high, it can lead to not only a failure to achieve the expected positive returns but also result in losses. The final section provides directions for future work.

關鍵字(中)

★ 資金管理
★ 凱利準則
★ 選擇權價差組合交易
★ 文斯最佳出價比例
★ 可盈利的
★ 最佳出價比例

關鍵字(英)

★ Money management
★ Kelly criterion
★ option spread trading
★ Vince′s Optimal fraction
★ profitable
★ optimal bidding fraction

論文目次

中文摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 v
表目錄 vii
一、緒論 1
1-1 研究動機 1
1-2 研究目的 3
1-3 研究架構 4
二、預備知識 5
2-1 凱利準則 5
2-2 文斯的最佳f值 8
三、選擇權價差組合的最佳比例 11
3-1 尋找有利的選擇權價差組合 11
3-2 最有利的選擇權組合演算法 18
四、進行模擬實驗 19
4-1 買權價差 19
4-2 賣權價差 24
4-3 雙賣價差 29
4-4 實驗結果整理 33
五、結論 34
Bibliographies 35

參考文獻

Bibliographies
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[2] Chou, Y.H., et al., “Portfolio Optimization Based on Funds Standardization and Genetic Algorithm”, Ieee Access, 5, 2017, pp. 21885-21900.
[3] Chou, Y. H., et al., “A Rule-Based Dynamic Decision-Making Stock Trading System Based on Quantum-Inspired Tabu Search Algorithm”, Ieee Access, 2, 2014, pp. 883-896.
[4] Gottlieb, G., “An optimal betting strategy for repeated games”, Journal of Applied Probability, 22.4, 1985, pp. 787-795.
[5] Hsieh, C.-H. and B.R. Barmish. “On Kelly betting: some limitations”, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2015, pp. 165-172.
[6] Hsieh, C.-H., et al., “Kelly betting can be too conservative”, 2016 IEEE 55th conference on decision and control (CDC). IEEE, 2016, pp. 3695-3701.
[7] Kelly, J.L., “A new interpretation of information rate”, the bell system technical journal, 35.4, 1956, pp. 917-926.
[8] Kullback, S. and R. Leibler, “On information and sufficiency”, The annals of mathematical statistics, 22(1), 1951, pp. 79–86.
[9] MacLean, L.C. , et al., “Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria”, Quantitative Finance, 10(7), 2010, pp. 681–687.
[10] ──────, The Kelly capital growth investment criterion: Theory and practice, Vol. 3, world scientific, 2011.
[11] Stutzer, M., "On growth-optimality vs. security against underperformance”, The Kelly capital growth investment criterion: theory and practice, 2011, pp. 641-653.
[12] Thorp, E.O., “The Kelly criterion in blackjack sports betting, and the stock market”, Handbook of asset and liability management, North-Holland, 2008, pp. 385-428.
[13] ──────, “Understanding the Kelly criterion”, The Kelly capital growth investment criterion: theory and practice, 2011, pp. 509-523.
[14] Vince, R., Portfolio management formulas: mathematical trading methods for the futures, options, and stock markets, Vol. 1, John Wiley & Sons, 1991.
[15] ──────, The mathematics of money management: risk analysis techniques for traders, Vol. 18, John Wiley & Sons, 1992.
[16] ──────, The new money management: a framework for asset allocation, Vol. 47, John Wiley & Sons, 1995.
[17] ──────, The leverage space trading model: reconciling portfolio management strategies and economic theory, John Wiley and Sons, 2009.
[18] Wu, M.-E., et al. “An adaptive Kelly betting strategy for finite repeated games”, International conference on genetic and evolutionary computing, Spriger International Publishing, 2015.
[19] Wu, M.-E., et al., “An Empirical Comparison between Kelly Criterion and Vince′s Optimal F”, 2015 IEEE International Conference on Smart City/SocialCom/SustainCom (SmartCity), IEEE, 2015, pp. 806-810.
[20] Wu, M.E. and W.H. Chung, “A Novel Approach of Option Portfolio Construction Using the Kelly Criterion”, Ieee Access, 6, 2018, pp. 53044-53052.
[21] Wu, M.E., et al., “Using trading mechanisms to investigate large futures data and their implications to market trends”, Soft Computing, 21, 2017, pp. 2821-2834.

指導教授

黃泓人吳庭斌(Hong-ren Huang Ting-Pin Wu)

審核日期

2023-7-10

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