機器學習在美式選擇權定價的應用

Application of Machine Learning to the Pricing of American Options

蔡旻浩(Min-Hao Cai)

指導教授 ： 羅盛豐

中原大學/商學院/財務金融研究所/碩士(2022年)

https://doi.org/10.6840/cycu202200117

摘要

本文利用蒙地卡羅法來生成股價資料，並透過機器學習的應用來達成美式選擇權的訂價。由於透過蒙地卡羅法來評價美式選擇權存在股價路徑上的最適執行點問題，因此本文先寫下一方程式作為分類器，用以判斷每條股價路徑中的各個時間點執行與否，並選擇第一個執行時間點進行該點股價的折現，進一步得到選擇權的價格。接著使用優化器解出在使選擇權價格最大化下的方程式，而透過該方程式回推出每條價格路徑中的每一點該價格是否提早執行，建立執行與否的標籤。最後使用機器學習方法中用以解決分類問題的羅吉斯回歸模型，將每一筆資料的時間點、股價以及執行標籤作為訓練資料，透過機器學習得到新的分類器後再次模擬出新的股價資料並計算選擇權價格，最後得到非常近似真值的美式選擇權價格。

關鍵字

美式選擇權定價 ； 蒙地卡羅模擬 ； 機器學習 ； 羅吉斯回歸

並列摘要

This study focuses on the pricing of American-style options with Monte Carlo Method. We first presume the stopping boundary takes a particular function form and use an optimizer to determine the optimal coefficients associated. Then we use the obtained stopping rule to find out the first point of time of early exercise for each sample path and work out the option value by averaging the present value of exercise proceeds at these time points. Since we borrow a parsimonious model for the stopping rule, bias must exist in the pricing results, especially for the out-of-sample cases. We hence try to improve the pricing performance by considering a machine learning method. Specifically, we apply logistic regression algorithm to amend the stopping rule so that more precise out-of-sample prices can be attained. Numerical examples show the feasibility of our approach, which is also valid even for 100 simulated paths only.

並列關鍵字

American-style options ； Bermudan options ； Monte Carlo simulation ； Machine Learning ； Logistic Regression Algorithm

參考文獻

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