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    题名: 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
    贡献者: 江彌修
    Chiang, Mi-Hsiu
    許琳
    Xu, Lin
    关键词: 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
    上传时间: 2019-07-01 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.
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    [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.
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    [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
    数据类型: thesis
    DOI: 10.6814/NCCU201900058
    显示于类别:[金融學系] 學位論文

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