風險測度轉換下之GARCH選擇權評價

Abstract

使用殘差機率分配抽樣的過濾歷史模擬法可以作為未來資產價格的預測，而風險中立假設不適當的問題則可透過風險測度的轉換予以解決，該轉換過程係將市場價格與模型價格的均方差極小化求得估計校正後的新參數，作為狀態價格機率分配的轉換機制。本研究目的係探討在非常態與無特定分配設定下的GARCH選擇權定價，透過狀態價格機率分配及其校正，即可估計風險中立下的校正參數。實證結果指出，透過校正參數的模擬，平均定價誤差絕對值以及誤差均方和皆能有效地降低，此外，經過校正後的風險中立機率分配及與透過歷史資料參數分配下的訂價結果相異。

Asset future prices can be forecasted with filtering historical simulation by drawing from standardized residual density. The problem of inappropriate risk neutral assumption could be resolved by the calibration from density transformation. The transformation is to identify the state price density per unit probability through the parameter re-estimation by minimizing the mean squared error of market and model prices. The purpose of the research is to price the GARCH options without risk neutral assumption and the specification of state price density per unit probability. The FHS with calibration is employed to estimate risk neutral parameters. The empirical results show that the average absolute pricing error and the sum of squared error are reduced with the simulation from calibrated parameters. Another finding is that the risk neutral pricing densities with calibration are different from the pricing under historical measure ones due to investors' preferences and risk premium.