隨機波動度Heath-Jarrow-Morton模型下之利率衍生性商品評價

Pricing Interest Rate Derivatives in Heath-Jarrow-Morton Model with Stochastic Volatility

譚立暉(Lap Fai, Tam)

指導教授 ： 李賢源

共同指導教授 ： 石百達

國立臺灣大學/管理學院/財務金融學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02768

摘要

本文提供了一個靈活的多因子隨機波動度Heath–Jarrow–Morton模型，此模型讓遠期利率與其波動度具有相關性，且有N個隨機因子會影響利率結構，另有額外N個隨機因子會影響波動度(及利率衍生性商品)。此模型改進了Trolle and Schwartz (2009)的模型，讓利率波動度與短期利率(short rate)水準有正比關係。此模型能夠轉換成有限狀態變數(finite number of state variables)的馬可夫表現(Markov representation)系統，故能輕易地使用蒙地卡羅模擬法來評價各種利率衍生性產品，如利率上限選擇權、利率交換選擇權等。最後我們會分析各參數對評價結果的影響。

關鍵字

Heath-Jarrow-Morton模型 ； 隨機波動度 ； 狀態依賴波動度 ； 蒙地卡羅模擬法 ； 利率上限選擇權

並列摘要

This article provides a flexible stochastic volatility multi-factor Heath–Jarrow–Morton term structure model, which allows forward rate correlative with its volatility, and there are N random factors affect the interest rate structure, while additional N random factors would affect volatilities (and also interest rate derivatives). This model improves the Trolle and Schwartz (2009) model, so that interest rate volatility is proportional to the short rate. This model can be converted into a finite-state variables Markov representation system, so under this model, Monte Carlo simulation can be easily used to evaluate the various interest rate derivatives, such as interest rate cap, swaption, etc.. Finally, we will analyze the impact of various parameters on the pricing result.

並列關鍵字

Heath-Jarrow-Morton model ； Stochastic volatility ； State dependent volatility ； Monte Carlo simulation ； Caps

參考文獻

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Ball, C. A., and W. N. Torous, 1999. The Stochastic Volatility of Short-Term Interest Rates: Some International Evidence, The Journal of Finance 54, 2339-2359.

Bhar, R., and C. Chiarella, 1997. Transformation of Heath-Jarrow-Morton models to Markovian systems, The European Journal of Finance 3, 1 - 26.

Bhar, R., C. Chiarella, N. El-Hassan, and X. Zheng, 2000. The reduction of forward rate dependent volatility HJM models to Markovian form: Pricing European bond options, Journal of Computational Finance 3, 47.