Pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck process

2015 ◽  
Vol 28 (6) ◽  
pp. 1412-1425 ◽  
Author(s):  
Zhaoli Jia ◽  
Xiuchun Bi ◽  
Shuguang Zhang
Keyword(s):  
Stochastic Volatility ◽  
Uhlenbeck Process ◽  
Variance Swaps ◽  
Ornstein Uhlenbeck Process

scholarly journals AN ANALYTICAL APPROACH FOR VARIANCE SWAPS WITH AN ORNSTEIN–UHLENBECK PROCESS

2017 ◽  
Vol 59 (1) ◽  
pp. 83-102
Author(s):  
JIAN-PENG CAO ◽  
YAN-BING FANG
Keyword(s):  
Factor Model ◽  
Discrete Models ◽  
Heston Model ◽  
Uhlenbeck Process ◽  
Variance Swaps ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Return Variance ◽  
Mc Simulation ◽  
Popular Subject

Pricing variance swaps have become a popular subject recently, and most research of this type come under Heston’s two-factor model. This paper is an extension of some recent research which used the dimension-reduction technique based on the Heston model. A new closed-form pricing formula focusing on a log-return variance swap is presented here, under the assumption that the underlying asset prices can be described by a mean-reverting Gaussian volatility model (Ornstein–Uhlenbeck process). Numerical tests in two respects using the Monte Carlo (MC) simulation are included. Moreover, we discuss a procedure of solving a quadratic differential equation with one variable. Our method can avoid the previously encountered limitations, but requires more time for calculation than other recent analytical discrete models.

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.

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