THE PRICING OF EUROPEAN OPTIONS UNDER THE CONSTANT ELASTICITY OF VARIANCE WITH STOCHASTIC VOLATILITY

2013 ◽  
Vol 12 (01) ◽  
pp. 1350004 ◽  
Author(s):  
BOUNGHUN BOCK ◽  
SUN-YONG CHOI ◽  
JEONG-HOON KIM
Keyword(s):  
Numerical Experiment ◽  
Stochastic Volatility ◽  
Hybrid Model ◽  
Multiscale Analysis ◽  
Asset Price ◽  
European Options ◽  
Barrier Option ◽  
Price Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance

This paper considers a hybrid risky asset price model given by a constant elasticity of variance multiplied by a stochastic volatility factor. A multiscale analysis leads to an asymptotic pricing formula for both European vanilla option and a Barrier option near the zero elasticity of variance. The accuracy of the approximation is provided in a rigorous manner. A numerical experiment for implied volatilities shows that the hybrid model improves some of the well-known models in view of fitting the data for different maturities.

COMPUTATION OF VOLATILITY IN STOCHASTIC VOLATILITY MODELS WITH HIGH FREQUENCY DATA

2010 ◽  
Vol 13 (05) ◽  
pp. 767-787 ◽  
Author(s):  
EMILIO BARUCCI ◽  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Asset Price ◽  
Heston Model ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Price Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Correlation Parameters

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

scholarly journals Option pricing under a discrete-time Markov switching stochastic volatility with co-jump model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Michael C. Fu ◽  
Bingqing Li ◽  
Rongwen Wu ◽  
Tianqi Zhang
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Asset Price ◽  
Markov Switching ◽  
European Options ◽  
Computationally Efficient ◽  
Volatility Clustering ◽  
European Option Pricing ◽  
Jump Model

<p style='text-indent:20px;'>We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can capture asset price features such as leptokurtosis, skewness, volatility clustering, and varying mean-reversion speed of volatility. For pricing European options, we develop a computationally efficient method for obtaining the probability distribution of average integrated variance (AIV), which is key to option pricing under stochastic-volatility-type models. Building upon the efficiency of the European option pricing approach, we are able to price an American-style option, by converting its pricing into the pricing of a portfolio of European options. Our work also provides constructive guidance for analyzing derivatives based on variance, e.g., the variance swap. Numerical results indicate our methods can be implemented very efficiently and accurately.</p>

scholarly journals LEFT-WING ASYMPTOTICS OF THE IMPLIED VOLATILITY IN THE PRESENCE OF ATOMS

2015 ◽  
Vol 18 (02) ◽  
pp. 1550013 ◽  
Author(s):  
ARCHIL GULISASHVILI
Keyword(s):  
Asymptotic Formula ◽  
Implied Volatility ◽  
Asset Price ◽  
First Hitting Time ◽  
Left Wing ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Price Distribution ◽  
New Formula

The paper considers the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant elasticity of variance (CEV) model, jump-to-default models, and stochastic models described by processes stopped at the first hitting time of zero. For models with atoms, the behavior of the implied volatility at large strikes is similar to that in models without atoms. On the other hand, the behavior of the implied volatility at small strikes is influenced significantly by the atom at zero. De Marco, Hillairet, and Jacquier found an asymptotic formula for the implied volatility at small strikes with two terms and also provided an incomplete description of the third term. In the present paper, we obtain a new asymptotic formula for the left wing of the implied volatility, which is qualitatively different from the De Marco–Hillairet–Jacquier formula. The new formula contains three explicit terms and an error estimate. In the paper, we show how to derive the De Marco–Hillairet–Jacquier formula from the new formula, and compare the performance of the two formulas in the case of the CEV model. The graphs included in the paper show that the new asymptotic formula provides a notably better approximation to the implied volatility at small strikes in the CEV model than the De Marco–Hillairet–Jacquier formula.

scholarly journals Leverage Effect and Stochastic Volatility in the Agricultural Commodity Market under the CEV Model

2017 ◽  
Vol 65 (5) ◽  
pp. 1671-1678
Author(s):  
Michal Čermák
Keyword(s):  
Stochastic Volatility ◽  
Generalized Method Of Moments ◽  
Commodity Prices ◽  
Commodity Price ◽  
Leverage Effect ◽  
Commodity Market ◽  
Agricultural Commodity ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance

The problem of price fluctuation is crucial to the concept of financial engineering nowadays. The aim of this paper is twofold; first to investigate the leverage effect of the main agricultural commodities – wheat and corn, i. e. the relationship between monetary returns and the volatility of commodity prices and, secondly to capture their stochastic volatility by forming an appropriate model. The data are considered as ‘post‑crisis’ data. That means the period after the biggest shock to the world economy. Thus, the Constant Elasticity of Variance (CEV) model is used calibrated to the Generalized Method of Moments (GMM). The paper is briefly based on the research of Geman and Shih (2009), who propose an extension in capturing the leverege effect in the commodity market. Their results show a positive relationship between commodity price returns and the volatility in both the corn and wheat derivative market. According to these results, corn futures prices are characterized significantly under the CEV model. On the other side in the wheat futures market exists a driftless condition by using stochastic volatility models.

scholarly journals Efficient exponential timestepping algorithm using control variate technique for simulating a functional of exit time of one-dimensional Brownian diffusion with applications in finance

2020 ◽  
Vol 9 (3) ◽  
pp. 495-511
Author(s):  
Hasan Alzubaidi
Keyword(s):  
Variance Reduction ◽  
Exit Time ◽  
Statistical Error ◽  
Original Method ◽  
Brownian Diffusion ◽  
Barrier Option ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Control Variate

Abstract The exponential timestepping Euler algorithm with a boundary test is adapted to simulate an expected of a function of exit time, such as the expected payoff of barrier options under the constant elasticity of variance (CEV) model. However, this method suffers from a high Monte Carlo (MC) statistical error due to its exponentially large exit times with unbounded samples. To reduce this kind of error efficiently and to speed up the MC simulation, we combine such an algorithm with an effective variance reduction technique called the control variate method. We call the resulting algorithm the improved Exp algorithm for abbreviation. In regard to the examples we consider in this paper for the restricted CEV process, we found that the variance of the improved Exp algorithm is about six times smaller than that of the Jansons and Lythe original method for the down-and-out call barrier option. It is also about eight times smaller for the up-and-out put barrier option, indicating that the gain in efficiency is significant without significant increase in simulation time.

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