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.

A NOVEL ANALYTICAL APPROACH FOR PRICING DISCRETELY SAMPLED GAMMA SWAPS IN THE HESTON MODEL

2016 ◽  
Vol 57 (3) ◽  
pp. 244-268
Author(s):  
SANAE RUJIVAN
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Analytical Approach ◽  
Solution Procedure ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Variance Swaps ◽  
Closed Form Solutions ◽  
Volatility Model ◽  
Closed Form Formula

The main purpose of this paper is to present a novel analytical approach for pricing discretely sampled gamma swaps, defined in terms of weighted variance swaps of the underlying asset, based on Heston’s two-factor stochastic volatility model. The closed-form formula obtained in this paper is in a much simpler form than those proposed in the literature, which substantially reduces the computational burden and can be implemented efficiently. The solution procedure presented in this paper can be adopted to derive closed-form solutions for pricing various types of weighted variance swaps, such as self-quantoed variance and entropy swaps. Most interestingly, we discuss the validity of the current solutions in the parameter space, and provide market practitioners with some remarks for trading these types of weighted variance swaps.

scholarly journals Asymptotic Exponential Arbitrage in the Schwartz Commodity Futures Model

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Tesfamariam Tadesse Welemical ◽  
Jane Akinyi Aduda ◽  
Martin Le Doux Mbele Bidima
Keyword(s):  
Failure Probability ◽  
Factor Model ◽  
Commodity Futures ◽  
Financial Security ◽  
Futures Prices ◽  
Uhlenbeck Process ◽  
Futures Contract ◽  
Asymptotic Arbitrage ◽  
Ornstein Uhlenbeck Process

In this paper, we consider the Schwartz’s one-factor model for a storable commodity and a futures contract on that commodity. We introduce the analysis of asymptotic arbitrage in storable commodity models by proving that the futures prices process allows asymptotic exponential arbitrage with geometric decaying failure probability. Next, we find by comparison that, under some similar conditions, our result is a corresponding commodity assets (stronger) version of Föllmer and Schachermayer’s result stated in the modeling setting of geometric Ornstein-Uhlenbeck process for financial security assets.

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.

A SIMPLE CLOSED-FORM FORMULA FOR PRICING DISCRETELY-SAMPLED VARIANCE SWAPS UNDER THE HESTON MODEL

2014 ◽  
Vol 56 (1) ◽  
pp. 1-27 ◽  
Author(s):  
SANAE RUJIVAN ◽  
SONG-PING ZHU
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Analytical Approach ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Model Parameters ◽  
Variance Swaps ◽  
Volatility Model ◽  
The Right ◽  
Closed Form Formula

AbstractWe develop a simplified analytical approach for pricing discretely-sampled variance swaps with the realized variance, defined in terms of the squared log return of the underlying price. The closed-form formula obtained for Heston’s two-factor stochastic volatility model is in a much simpler form than those proposed in literature. Most interestingly, we discuss the validity of our solution as well as some other previous solutions in different forms in the parameter space. We demonstrate that market practitioners need to be cautious, making sure that their model parameters extracted from market data are in the right parameter subspace, when any of these analytical pricing formulae is adopted to calculate the fair delivery price of a discretely-sampled variance swap.

scholarly journals Sensitivity analysis in the infinite dimensional Heston model

2021 ◽  
pp. 2150014
Author(s):  
Fred Espen Benth ◽  
Giulia Di Nunno ◽  
Iben Cathrine Simonsen
Keyword(s):  
Sensitivity Analysis ◽  
Representation Formula ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Forward Contracts ◽  
Uhlenbeck Process ◽  
Infinite Dimensional ◽  
Forward Price ◽  
Volatility Model ◽  
Forward Contract

We consider the infinite dimensional Heston stochastic volatility model proposed in Ref. 7. The price of a forward contract on a non-storable commodity is modeled by a generalized Ornstein–Uhlenbeck process in the Filipović space with this volatility. We prove a representation formula for the forward price. Then we consider prices of options written on these forward contracts and we study sensitivity analysis with computation of the Greeks with respect to different parameters in the model. Since these parameters are infinite dimensional, we need to reinterpret the meaning of the Greeks. For this we use infinite dimensional Malliavin calculus and a randomization technique.

scholarly journals Modeling Wind Speed Based on Fractional Ornstein-Uhlenbeck Process

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5561
Author(s):  
Sergey Obukhov ◽  
Ahmed Ibrahim ◽  
Denis Y. Davydov ◽  
Talal Alharbi ◽  
Emad M. Ahmed ◽  
...  
Keyword(s):  
Wind Speed ◽  
Power Plants ◽  
Moving Average ◽  
Discrete Models ◽  
Model Parameters ◽  
Observation Data ◽  
Time Step ◽  
Uhlenbeck Process ◽  
Wind Speeds ◽  
Ornstein Uhlenbeck Process

The primary task of the design and feasibility study for the use of wind power plants is to predict changes in wind speeds at the site of power system installation. The stochastic nature of the wind and spatio-temporal variability explains the high complexity of this problem, associated with finding the best mathematical modeling which satisfies the best solution for this problem. In the known discrete models based on Markov chains, the autoregressive-moving average does not allow variance in the time step, which does not allow their use for simulation of operating modes of wind turbines and wind energy systems. The article proposes and tests a SDE-based model for generating synthetic wind speed data using the stochastic differential equation of the fractional Ornstein-Uhlenbeck process with periodic function of long-run mean. The model allows generating wind speed trajectories with a given autocorrelation, required statistical distribution and provides the incorporation of daily and seasonal variations. Compared to the standard Ornstein-Uhlenbeck process driven by ordinary Brownian motion, the fractional model used in this study allows one to generate synthetic wind speed trajectories which autocorrelation function decays according to a power law that more closely matches the hourly autocorrelation of actual data. In order to demonstrate the capabilities of this model, a number of simulations were carried out using model parameters estimated from actual observation data of wind speed collected at 518 weather stations located throughout Russia.

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