scholarly journals Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process

2020 ◽  
Vol 21 (2) ◽  
pp. 173-187
Author(s):  
Piotr Szczepocki
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Models ◽  
Uhlenbeck Process ◽  
Volatility Models ◽  
Ornstein Uhlenbeck Process ◽  
Non Gaussian ◽  
Iterated Filtering

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.

scholarly journals PRICING AND HEDGING OF VIX OPTIONS FOR BARNDORFF-NIELSEN AND SHEPHARD MODELS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950043 ◽  
Author(s):  
TAKUJI ARAI
Keyword(s):  
Fourier Transform ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Option Price ◽  
Call Option ◽  
Stochastic Volatility Models ◽  
Risky Assets ◽  
Volatility Models ◽  
Vix Options ◽  
Non Gaussian

The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein–Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.

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.

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