scholarly journals Stochastic Volatility With an Ornstein-Uhlenbeck Process: An Extension

1998 ◽  
Author(s):  
Rainer Schoebel ◽  
Jianwei Zhu
Keyword(s):  
Stochastic Volatility ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process

On American Derivatives and Related Obstacle Problems

2003 ◽  
Vol 06 (06) ◽  
pp. 565-591 ◽  
Author(s):  
Jörg Kampen
Keyword(s):  
Interest Rates ◽  
Stochastic Volatility ◽  
Obstacle Problems ◽  
Stochastic Volatility Models ◽  
Uhlenbeck Process ◽  
Typical Situation ◽  
Motion Models ◽  
Volatility Models ◽  
Ornstein Uhlenbeck Process ◽  
Classical Models

We derive obstacle problems for pricing of American derivatives with multiple underlyings heuristically using only a few postulates such that classical (Brownian motion) models as well as models based on Levy processes can be considered in our frame. For the classical models we define a "signed measure" which allows to compute the exercise region near maturity and obtain a generic condition for continuity of the free boundary and prove some more general features of exercise regions for classical models. Especially, we investigate the exercise regions of the most important American derivatives with one and multiple underlyings where we include dependence of volatility and interest rates on time and the underlyings extending and recovering some classical results. Further applications include stochastic volatility models. It is shown that in classical stochastic volatility models where volatility is driven by an Ornstein-Uhlenbeck process an American compound call has a nonempty exercise region and compute the exercise region near expiration in a typical situation.

GENERALIZED BARNDORFF-NIELSEN AND SHEPHARD MODEL AND DISCRETELY MONITORED OPTION PRICING

2016 ◽  
Vol 19 (04) ◽  
pp. 1650024 ◽  
Author(s):  
AKIRA YAMAZAKI
Keyword(s):  
Stochastic Volatility ◽  
Joint Distribution ◽  
Closed Form Expression ◽  
European Options ◽  
Form Expression ◽  
Uhlenbeck Process ◽  
Lookback Options ◽  
Ornstein Uhlenbeck Process ◽  
Path Dependent ◽  
Non Gaussian

This paper proposes a generalization of the Barndorff-Nielsen and Shephard model, in which the log return on an asset is governed by a Lévy process with stochastic volatility modeled by a non-Gaussian Ornstein–Uhlenbeck process. Under the generalized model, we derive a closed-form expression of the multivariate characteristic function of the intertemporal joint distribution of the underlying log return. Then, we also investigate asymptotic behavior of the log return and its variance. Moreover, we evaluate discretely monitored path-dependent derivatives such as geometric Asian, forward start, barrier, fade-in, and lookback options as well as European options.

scholarly journals A CORRELATED STOCHASTIC VOLATILITY MODEL MEASURING LEVERAGE AND OTHER STYLIZED FACTS

2002 ◽  
Vol 05 (05) ◽  
pp. 541-562 ◽  
Author(s):  
JAUME MASOLIVER ◽  
JOSEP PERELLÓ
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
Leverage Effect ◽  
Stylized Facts ◽  
Uhlenbeck Process ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Negative Skewness

We analyze a stochastic volatility market model in which volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. In the framework of this model we exactly calculate the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.

scholarly journals Turbo Warrants under Hybrid Stochastic and Local Volatility

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Min-Ku Lee ◽  
Ji-Hun Yoon ◽  
Jeong-Hoon Kim ◽  
Sun-Hwa Cho
Keyword(s):  
Stochastic Volatility ◽  
Uhlenbeck Process ◽  
Variance Model ◽  
Constant Elasticity ◽  
Local Volatility ◽  
Constant Elasticity Of Variance ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Sensitive Structure

This paper considers the pricing of turbo warrants under a hybrid stochastic and local volatility model. The model consists of the constant elasticity of variance model incorporated by a fast fluctuating Ornstein-Uhlenbeck process for stochastic volatility. The sensitive structure of the turbo warrant price is revealed by asymptotic analysis and numerical computation based on the observation that the elasticity of variance controls leverage effects and plays an important role in characterizing various phases of volatile markets.

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