學(xué)術(shù)講座：The Alpha-Heston Stochastic Volatility Model

金融學(xué)院SBF論壇2019年第11講

講座題目：The Alpha-Heston Stochastic Volatility Model

時(shí)間：2019年5月6日（周一）12:20-13:30

地點(diǎn)：博學(xué)樓925

主講人：焦瑩

主講人簡(jiǎn)介：

焦瑩教授是里昂第一大學(xué)金融與精算科學(xué)研究所（Institute of Financial and Actuarial Sciences of University of Lyon 1）應(yīng)用數(shù)學(xué)教授。她的研究興趣包括金融數(shù)學(xué)和應(yīng)用概率，涵蓋金融和保險(xiǎn)領(lǐng)域的風(fēng)險(xiǎn)模型、隨機(jī)控制和優(yōu)化等。

講座內(nèi)容簡(jiǎn)介：

We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by α-stable processes with α ∈ (1, 2]. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. In particular, we show that the behavior of stock implied volatility is the sharpest coherent with theoretical bounds at extreme strikes independently of the value of α ∈ (1, 2). As far as variance options are concerned, VIX2-implied volatility is characterized by an upward-sloping behavior and the slope is growing when α decreases. Furthermore, we examine the jump clustering phenomenon observed on the variance market and provide a decomposition formula which allows to analyse the cluster processes.

本文對(duì)Hestion模型進(jìn)行了仿射擴(kuò)展，其瞬時(shí)方差過(guò)程包含一個(gè)由α ∈ (1, 2]的α-穩(wěn)定過(guò)程驅(qū)動(dòng)的跳躍。在這個(gè)框架下，本文檢驗(yàn)了資產(chǎn)和方差期權(quán)的隱含波動(dòng)率及其漸進(jìn)性。特別的是，本文發(fā)現(xiàn)股票隱含波動(dòng)率的行為與極端沖擊下的理論邊界相一致，而與α ∈ (1, 2)的取值無(wú)關(guān)。當(dāng)考慮了方差期權(quán)時(shí)，VIX2隱含波動(dòng)性表現(xiàn)出向上傾斜的特征，當(dāng)α減小時(shí)，斜率增加。此外，本文檢驗(yàn)了方差的跳躍聚集現(xiàn)象，并給出了可以用來(lái)分析聚類(lèi)行為的分解方差。