應用深度強化學習於考量交易成本之選擇權避險

Deep Reinforcement Learning in Option Hedging with Transaction Costs

許顥騰(Hao-Teng Hsu)

指導教授 ： 呂育道

國立臺灣大學/電機資訊學院/資訊工程學系/碩士(2023年)

https://doi.org/10.6342/NTU202301613

摘要

本研究為利用深度強化學習來為選擇權避險，在考量交易成本下透過模擬市場資料來學習避險策略。我們採用了近端策略優化 (proximal policy optimization, PPO) 演算法，分別利用 Black-Scholes 模型與 Heston 模型產生的市場資料進行學習。此外，我們以 Leland (1985) 的避險策略做為對照，並比較避險後的損益分布。研究結果顯示，在 Black-Scholes 模型下，PPO 學習到了與 Leland 近似的策略；而在 Heston 模型下，PPO 的損益分布平均值相較於 Leland 更接近零，但標準差則較大。

關鍵字

深度強化學習 ； 交易成本 ； 選擇權避險 ； Leland 避險策略 ； Black-Scholes 模型 ； Heston 模型

並列摘要

This study employs deep reinforcement learning for option hedging with transaction costs by learning hedging strategies through simulated market data. We utilize the proximal policy optimization (PPO) algorithm for both the Black-Scholes and Heston models. The Leland (1985) hedging strategy is used as a benchmark for comparing the profit and loss distributions of the hedging strategies. The results indicate that PPO can learn a strategy that approximates Leland’s approach under the Black-Scholes model. Under the Heston model, PPO’s average profit and loss is closer to zero than Leland’s strategy but has a slightly larger standard deviation.

並列關鍵字

Deep reinforcement learning ； Transaction costs ； Option hedging ； Leland hedging strategy ； Black-Scholes model ； Heston model

參考文獻

[1] L. Andersen. Simple and Efficient Simulation of the Heston Stochastic Volatility Model. Journal of Computational Finance, 11(3):1–42, Mar. 2008.

[2] F. Black and M. Scholes. The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3):637–654, 1973.

[3] P. P. Boyle and T. Vorst. Option Replication in Discrete Time with Transaction Costs. Journal of Finance, 47(1):271–293, 1992.

[4] H. Buehler, L. Gonon, J. Teichmann, and B. Wood. Deep Hedging. Quantitative Finance, 19(8):1271–1291, Aug. 2019.

[5] J. Cao, J. Chen, J. Hull, and Z. Poulos. Deep Hedging of Derivatives Using Reinforcement Learning. Journal of Financial Data Science, 3(1):10–27, Jan. 2021.