SABR模型下使用遠期及選擇權資料的參數估計

Estimation under SABR Model using both Forward and Option Data

張正鉉(Cheng-Syuan Chang)

指導教授 ： 傅承德

國立中央大學/理學院/統計研究所/碩士(2011年)

摘要

本篇論文中我們使用SABR模型做為標的資產模型，藉由Black -Scholes歐式選擇權定價公式，SABR模型下對於Black-Scholes公式的隱含波動度具有封閉解的形式，接著我們考慮二種情況下的參數估計：首先考慮遠期契約價格以及波動度可觀測的情況，接著我們考慮波動度不可觀測的情況下，使用選擇權資料取代不可觀測的波動度，並以Aït-Sahalia提出變數變換的方式求得近似概似函數。最後以最大概似估計法求得參數的估計值，並以蒙地卡羅模擬比較整體性的結果。

關鍵字

SABR模型 ； 波動度 ； 最大概似估計法 ； 蒙地卡羅模擬

並列摘要

We model the underlying asset with SABR model. According to the Black-Scholes formula, the implied volatility under the SABR model has a closed-form formula. Then we consider about the estimation as the volatility is observable or not. When the volatility is unobservable, the volatility state is replaced by proxies based on the implied volatility. Finally we obtain the estimator by applying the maximum likelihood estimator, and use the Monte Carlo simulation to complete the research.

並列關鍵字

SABR model ； Volatility ； Maximum likelihood estim

參考文獻

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