運用線性規劃於選擇權交易策略與隱含波動率預測

Abstract

隨著選擇權知識的普及，許多投資人已經懂得使用不同的選擇權組合來獲取利潤，然而其操作方式依舊是基於其對於標的物價格走勢的判斷來選擇相對應的選擇權組合，以波動率為獲利來源之選擇權策略則較少被投資人所採用。 一般而言，以波動率變動為獲利來源之選擇權策略可以拆分為「選擇權交易策略」以及「波動率預測模型」這兩個部分，在選擇權交易策略方面，最常見的投資組合即為跨式以及勒式策略，然而在實際的交易中，這些策略的資金利用方式並非最有效率，同時也無法完全抵銷價格風險；而在波動率預測方面，多數的時間序列預測模型方向性正確率偏低，使得交易無法取得正報酬。 本研究將建立多個選擇權交易策略，其中包括以線性規劃來建構組合之策略，除此之外，本研究也會建立多個波動率預測模型，並且逐一將多個經濟變數納入模型中。透過將所有的策略及模型搭配來執行交易回測，我們可以從交易結果來檢驗以波動率為獲利來源之選擇權策略是否有獲利的可能，同時找到最適合這類策略的選擇權交易策略以及波動率預測模型。 研究結果顯示，不論是單獨執行看多或者看空波動率策略，或者同時執行兩方向之交易策略皆有可能取得正報酬，在看多波動率方向表現最佳的組合其年化報酬率為57.3%；在看空波動率方向表現最佳的組合其年化報酬率為27.6%；若將兩者合併，同時執行最佳看多及看空波動率策略，得到的年化報酬率為90.0%，勝率為58.3%。在選擇權交易策略方面，在看多波動率方向上，使用線性規劃策略的表現必定優於勒式策略，而在空方向上兩者則無明顯優劣。在波動率預測模型方面，使用將台指期、S&P 500、匯率以及GARCH(1,1)過程納入考量，取樣為500日的ARIMA(1,1,1)模型來進行預測，並將其預測值運用於交易回測上將使得交易結果有最好的表現。

Along with the popularization of the knowledge of options, many investors already know how to use different combinations of options to obtain profits. However, most of the strategies so far are based merely on the expectation of the underlying asset price. The options trading strategy that profit from volatility changes is still less used by investors. In general, the options trading strategies that profit from volatility changes can be split into the “options trading strategy” and the “volatility forecasting model”. In terms of options trading strategy, the most common portfolios are straddle and strangle. However, in the practice of real transactions, the way these strategies use their funds are not the most efficient, and these strategies can not completely offset the price risk. In terms of volatility forecasting model, most of the time series forecasting model has a low correctness in direction, which makes the options trading strategy unable to obtain positive return. This study will establish multiple options trading strategies, including the strategies that use linear programming to construct their portfolio. In addition, this study will build multiple volatility forecasting models, and consider several economic variables as the exogenous variables of the models. By combining all the strategies and models to carry out the backtesting, we can examine whether the options trading strategy that profit from volatility changes can generate profits or not, and find the most suitable options trading strategy and volatility forecasting model for it. The result of the study shows that it is possible to obtain positive return, whether it is a long volatility trading or a short volatility trading, or both. The best combination of options trading strategy and volatility forecasting model in the long volatility trading has the annualized return of 57.3%; and the best combination in the short volatility trading has the annualized return of 27.6%. If combine these two strategies, the strategy that trades both long and short volatility has the annualized return of 90.0%, and winning rate of 58.3%. In terms of options trading strategy, in the long volatility trading, the strategies that applied linear programming perform better than strangle strategies, and in the short volatility trading, there is no obvious advantages and disadvantages. In terms of volatility forecasting model, Using the 500 days rolling samples and one-step-ahead forecasts of the ARIMA (1,1,1) model, which takes TAIEX futures, S&P 500, Taiwan dollar exchange rate and GARCH (1,1) process into account, to conduct the backtesting can generate best trading result.