An analytical approach for variance swaps with an Ornstein-Uhlenbeck process

2017 ◽  
Vol 59 ◽  
pp. 83
Author(s):  
Jianpeng Cao ◽  
Yan-Bing Fang
Keyword(s):  
Analytical Approach ◽  
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.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

scholarly journals Using the Ornstein–Uhlenbeck process to model the evolution of interacting populations

2017 ◽  
Vol 429 ◽  
pp. 35-45 ◽  
Author(s):  
Krzysztof Bartoszek ◽  
Sylvain Glémin ◽  
Ingemar Kaj ◽  
Martin Lascoux
Keyword(s):  
Uhlenbeck Process ◽  
Interacting Populations ◽  
Ornstein Uhlenbeck Process

On the reflected Ornstein–Uhlenbeck process with catastrophes

2012 ◽  
Vol 218 (23) ◽  
pp. 11570-11582 ◽  
Author(s):  
V. Giorno ◽  
A.G. Nobile ◽  
R. di Cesare
Keyword(s):  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process
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