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題名 強化學習應用於美式選擇權評價
Applying Reinforcement Learning to American Option Pricing作者 許琳
Xu, Lin貢獻者 江彌修
Chiang, Mi-Hsiu
許琳
Xu, Lin關鍵詞 美式選擇權
定價
強化學習
最小平方策略迭代
最小平方蒙地卡羅法
American option
Pricing
Reinforcement learning
LSPI
FQI
LSM日期 2019 上傳時間 1-Jul-2019 10:48:51 (UTC+8) 摘要 本文研究了強化學習應用於美式選擇權定價問題，首先，使用 Li, Szepesvari and Schuurmans 提出之最小平方策略迭代(LSPI)演算法學習美式賣權履約策略並進行定價，將蘋果公司美式股票選擇權之真實市場數據處理後套用於 LSPI 方法，並將 LSPI 方法與 Tsitsiklis and Van Roy提出之FQI方法和傳統最小平方蒙地卡羅法比較定價準確性。其次，使用符合金融市場之分析方式，將賣權分價內外不同情況分析，並進行敏感度分析，觀察強化學習使用之參數對於定價結果之影響。模擬結果表示，LSPI 方法與 FQI 方法 總體優於 LSM 方法，強化學習對於愈價內之賣權定價愈準確。本文發現強化學習在商品定價領域仍有很大研究潛力，特別是模擬路徑方式與執行動作多樣性方面值得進一步討論。
In this paper we apply the reinforcement learning method to American options pricing. We mainly consider the least squares policy iteration (LSPI) proposed by Li, Szepesvari and Schuurmans(2009) to learn the exercise policy and pricing method of American put options. We price AAPL American stock option with processed real market data, and compare the accuracy between LSPI, FQI proposed by Tsitsiklis and Van Roy(2001), and the standard least square Monte Carlo method (LSM). In order to investigate the influence of parameters used in LSPI on pricing results, the analysis method in financial market, sensitivity analysis is carried out under different situations which are divided according to whether the put option is in-the-money or out-of-the-money. The simulation result shows that LSPI and FQI are superior to LSM in general, and LSPI is more accurate in pricing deeper in-the-money put option. We also find that the reinforcement learning method still has great research potential in the field of derivatives pricing. In particular, there is a need for further investigation on simulation method of price path or selecting action variety.參考文獻 [1] Barone-Adesi, G. and Whaley, R. (1987). Efficient Analytical Approximation of American Option Values. Journal of Finance, Vol. 42, 301-320.[2] Bellman, R. (1957). A Markovian Decision Process. Journal of Mathematics and Mechanics, Vol. 6, 679–684.[3] Black, F. and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, Vol. 81, 637-659.[4] Boyle, P. P. (1977). Options: A Monte Carlo Approach. Journal of Financial Economics, Vol. 4, 323–338.[5] Boyle, P. P. (1986). A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, Vol. 23(1), 1-12.[6] Brennan, M. and Schwartz, E. (1977). The Valuation of American Put Options. Journal of Finance, Vol. 32, 449-462.[7] Cox, J. C., Ross S. A. and Rubinstein, M. (1979). Option Pricing: A simplified Approach. Journal of Financial Economics, Vol. 7, 229-264.[8] Dubrov, B. (2015). Monte Carlo Simulation with Machine Learning for Pricing American Options and Convertible Bonds. SSRN.[9] Geske, R. (1979). The Valuation of Compound Options. Journal of Financial Economics, Vol. 7, 63–81.[10] Geske, R. (1979). A Note on an Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends. Journal of Financial Economics, Vol. 7, 275–380.[11] Geske, R. (1981). Comments on Whaley’s Note. Journal of Financial Economics, Vol. 9, 213–215.[12] Geske, R. and Johnson, H. E. (1984). The American Put Valued Analytically. Journal of Finance, Vol. 39, 1511-1524.[13] Haug, E.G., Haug, J. and Lewis, A. (2003). Back to Basics: a New Approach to the Discrete Dividend Problem. Wilmott Magazine, 37–47.[14] Howard, R. A. (1960). Dynamic Programming and Markov Processes. Cambridge, Mass: MIT Press.[15] Hull, J. C. (2011). Options, Futures, and Other Derivatives, 8th edition. United States of America: Prentice Hall.[16] Johnson, H. (1983). An Analytical Approximation for the American Put Price. Journal of Financial and Quantitative Analysis, Vol. 18, 141-148.[17] Ju., N. and Zhong, R. (1998). An Approximate Formula for Pricing American Options. Review of Financial Studies, Vol. 11, 627-646.[18] Lagoudakis, M. G. and Parr, R. (2003). Least-Squares Policy Iteration. Journal of Machine Learning Research , Vol. 4, 1107 – 1149.[19] Li, Y., Szepesvari, C. and Schuurmans, D. (2009). Learning Exercise Policies for American Options. In Proc. of the Twelfth International Conference on Artificial Intelligence and Statistics, JMLR: W&CP, Vol. 5, 352-359.[20] Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American options by simulation: a simple Least-Squares approach. Review Financial Studies, Vol. 14, 113-147.[21] Medvedev, A. and Scaillet, O. (2010). Pricing American options under stochastic volatility and stochastic interest rates. Journal of Financial Economics, Vol. 98, 145–159.[22] Merton, R. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, Vol. 2, 125–144.[23] Roll, R. (1977). An Analytical Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends. Journal of Financial Economics, Vol. 5, 251-258.[24] Tilley, J. A. (1993). Valuing American options in a path simulation model. Transactions of the Society of Actuaries, Vol. 45, 83–104.[25] Tsitsiklis, J. N. and Van Roy, B. (2001). Regression Methods for Pricing Complex American-style Options. IEEE Transactions on Neural Networks(special issue on computational finance), Vol. 12(4), 694–703.[26] Whaley, R. E. (1981). On the Valuation of American Call Options on Stocks with Known Dividends. Journal of Financial Economics, Vol. 10, 207–211.[27]陳戚光，（2001）。選擇權:理論.實務與應用。台灣：智勝文化。 描述 碩士
國立政治大學
金融學系
106352047資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106352047 資料類型 thesis dc.contributor.advisor 江彌修 zh_TW dc.contributor.advisor Chiang, Mi-Hsiu en_US dc.contributor.author (Authors) 許琳 zh_TW dc.contributor.author (Authors) Xu, Lin en_US dc.creator (作者) 許琳 zh_TW dc.creator (作者) Xu, Lin en_US dc.date (日期) 2019 en_US dc.date.accessioned 1-Jul-2019 10:48:51 (UTC+8) - dc.date.available 1-Jul-2019 10:48:51 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2019 10:48:51 (UTC+8) - dc.identifier (Other Identifiers) G0106352047 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124147 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融學系 zh_TW dc.description (描述) 106352047 zh_TW dc.description.abstract (摘要) 本文研究了強化學習應用於美式選擇權定價問題，首先，使用 Li, Szepesvari and Schuurmans 提出之最小平方策略迭代(LSPI)演算法學習美式賣權履約策略並進行定價，將蘋果公司美式股票選擇權之真實市場數據處理後套用於 LSPI 方法，並將 LSPI 方法與 Tsitsiklis and Van Roy提出之FQI方法和傳統最小平方蒙地卡羅法比較定價準確性。其次，使用符合金融市場之分析方式，將賣權分價內外不同情況分析，並進行敏感度分析，觀察強化學習使用之參數對於定價結果之影響。模擬結果表示，LSPI 方法與 FQI 方法 總體優於 LSM 方法，強化學習對於愈價內之賣權定價愈準確。本文發現強化學習在商品定價領域仍有很大研究潛力，特別是模擬路徑方式與執行動作多樣性方面值得進一步討論。 zh_TW dc.description.abstract (摘要) In this paper we apply the reinforcement learning method to American options pricing. We mainly consider the least squares policy iteration (LSPI) proposed by Li, Szepesvari and Schuurmans(2009) to learn the exercise policy and pricing method of American put options. We price AAPL American stock option with processed real market data, and compare the accuracy between LSPI, FQI proposed by Tsitsiklis and Van Roy(2001), and the standard least square Monte Carlo method (LSM). In order to investigate the influence of parameters used in LSPI on pricing results, the analysis method in financial market, sensitivity analysis is carried out under different situations which are divided according to whether the put option is in-the-money or out-of-the-money. The simulation result shows that LSPI and FQI are superior to LSM in general, and LSPI is more accurate in pricing deeper in-the-money put option. We also find that the reinforcement learning method still has great research potential in the field of derivatives pricing. In particular, there is a need for further investigation on simulation method of price path or selecting action variety. en_US dc.description.tableofcontents 第一章 簡介 1第二章 文獻回顧 5第三章 研究方法 8第一節 馬可夫決策過程MDP 9第二節 近似價值函數 14第三節 最小平方策略迭代LSPI 18第四節 美式選擇權定價 20（一） LSPI 20（二） FQI 23（三） 最小平方蒙地卡羅方法LSM 24（四） 基函數設定 25第四章 實證分析 27第一節 實證方法 27（一） 模型訓練方法 29（二） 模型套用及結果 31第二節 敏感度分析 42（一） 股價 42（二） 股價變動率 43（三） 股價波動率 44（四） 無風險利率 45第五章 結論與建議 46參考文獻 47 zh_TW dc.format.extent 2457193 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106352047 en_US dc.subject (關鍵詞) 美式選擇權 zh_TW dc.subject (關鍵詞) 定價 zh_TW dc.subject (關鍵詞) 強化學習 zh_TW dc.subject (關鍵詞) 最小平方策略迭代 zh_TW dc.subject (關鍵詞) 最小平方蒙地卡羅法 zh_TW dc.subject (關鍵詞) American option en_US dc.subject (關鍵詞) Pricing en_US dc.subject (關鍵詞) Reinforcement learning en_US dc.subject (關鍵詞) LSPI en_US dc.subject (關鍵詞) FQI en_US dc.subject (關鍵詞) LSM en_US dc.title (題名) 強化學習應用於美式選擇權評價 zh_TW dc.title (題名) Applying Reinforcement Learning to American Option Pricing en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Barone-Adesi, G. and Whaley, R. (1987). Efficient Analytical Approximation of American Option Values. Journal of Finance, Vol. 42, 301-320.[2] Bellman, R. (1957). A Markovian Decision Process. Journal of Mathematics and Mechanics, Vol. 6, 679–684.[3] Black, F. and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, Vol. 81, 637-659.[4] Boyle, P. P. (1977). Options: A Monte Carlo Approach. Journal of Financial Economics, Vol. 4, 323–338.[5] Boyle, P. P. (1986). A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, Vol. 23(1), 1-12.[6] Brennan, M. and Schwartz, E. (1977). The Valuation of American Put Options. Journal of Finance, Vol. 32, 449-462.[7] Cox, J. C., Ross S. A. and Rubinstein, M. (1979). Option Pricing: A simplified Approach. Journal of Financial Economics, Vol. 7, 229-264.[8] Dubrov, B. (2015). Monte Carlo Simulation with Machine Learning for Pricing American Options and Convertible Bonds. SSRN.[9] Geske, R. (1979). The Valuation of Compound Options. Journal of Financial Economics, Vol. 7, 63–81.[10] Geske, R. (1979). A Note on an Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends. Journal of Financial Economics, Vol. 7, 275–380.[11] Geske, R. (1981). Comments on Whaley’s Note. Journal of Financial Economics, Vol. 9, 213–215.[12] Geske, R. and Johnson, H. E. (1984). The American Put Valued Analytically. Journal of Finance, Vol. 39, 1511-1524.[13] Haug, E.G., Haug, J. and Lewis, A. (2003). Back to Basics: a New Approach to the Discrete Dividend Problem. Wilmott Magazine, 37–47.[14] Howard, R. A. (1960). Dynamic Programming and Markov Processes. Cambridge, Mass: MIT Press.[15] Hull, J. C. (2011). Options, Futures, and Other Derivatives, 8th edition. United States of America: Prentice Hall.[16] Johnson, H. (1983). An Analytical Approximation for the American Put Price. Journal of Financial and Quantitative Analysis, Vol. 18, 141-148.[17] Ju., N. and Zhong, R. (1998). An Approximate Formula for Pricing American Options. Review of Financial Studies, Vol. 11, 627-646.[18] Lagoudakis, M. G. and Parr, R. (2003). Least-Squares Policy Iteration. Journal of Machine Learning Research , Vol. 4, 1107 – 1149.[19] Li, Y., Szepesvari, C. and Schuurmans, D. (2009). Learning Exercise Policies for American Options. In Proc. of the Twelfth International Conference on Artificial Intelligence and Statistics, JMLR: W&CP, Vol. 5, 352-359.[20] Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American options by simulation: a simple Least-Squares approach. Review Financial Studies, Vol. 14, 113-147.[21] Medvedev, A. and Scaillet, O. (2010). Pricing American options under stochastic volatility and stochastic interest rates. Journal of Financial Economics, Vol. 98, 145–159.[22] Merton, R. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, Vol. 2, 125–144.[23] Roll, R. (1977). An Analytical Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends. Journal of Financial Economics, Vol. 5, 251-258.[24] Tilley, J. A. (1993). Valuing American options in a path simulation model. Transactions of the Society of Actuaries, Vol. 45, 83–104.[25] Tsitsiklis, J. N. and Van Roy, B. (2001). Regression Methods for Pricing Complex American-style Options. IEEE Transactions on Neural Networks(special issue on computational finance), Vol. 12(4), 694–703.[26] Whaley, R. E. (1981). On the Valuation of American Call Options on Stocks with Known Dividends. Journal of Financial Economics, Vol. 10, 207–211.[27]陳戚光，（2001）。選擇權:理論.實務與應用。台灣：智勝文化。 zh_TW dc.identifier.doi (DOI) 10.6814/NCCU201900058 en_US
