選擇權評價中外加訊息的作用:在跳躍擴散模型下的估計議題

Abstract

本論文在跳躍擴散模型中，以跳躍比例大小為非隨機的常數或對數常態分配此種特例，和選擇權價格的誤差與股價過程為獨立並且與理論公式存有常態誤差值的兩個假設下，去對模型中Winner過程(擴散)裡的σ以及Poisson過程(跳躍)裡的λ和δ，這幾個影響股價變異數的重要參數作討論。在股價資訊外加入選擇權的價格的資料，對估計模型裡的參數的精準度的影響為本論文的主要核心。 在論文中，跳躍比例分別以常數和對數常態分配的兩種情形下，以最大概似法估計參數。其中先只用股價資料來估計參數，以及股價資料加上選擇權資料來綜合估計參數，來做精準度的對比。從數值模擬的結果及經驗得知，並以費雪訊息數來做為估計好壞的一個參考指標，選擇權價格資料的加入，都能大幅的增加參數的統計推論的精準度。

In this paper, the main issue is about parameters involved with the stock’s volatility, which are the σ in the Winner (diffusion) process and the λ and δ in the Poisson (jump) process, under the special cases of jump diffusion models with two assumptions that are independence between option prices’ errors and stock and normal error between pricing formula and true price. The core of this paper is the improvement of the estimation accuracy by taking the option data into account together with the stock data. The special cases of Jump-Diffusion models, the constant and log-normal jump size, are adopted to investigate estimation issue by finding maximum likelihood estimators. To compare with the accuracy, we estimate the parameters by stock data only, and in the other hand, adding the option data. As the experience and the results from the numerical work and Fisher’s Information, the accuracy is improved indeed by adding option data.