The Estimation of Pricing Kernel of KOSPI 200 Options Under Stochastic Volatility

2007 ◽  
Vol 15 (1) ◽  
pp. 135-165
Author(s):  
Sang Il Han ◽  
Chang Hyun Yun
Keyword(s):  
Normal Distribution ◽  
Stochastic Volatility ◽  
Trading Volume ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Options Market ◽  
Negative Number ◽  
Pricing Kernel ◽  
Underlying Asset ◽  
Volatility Model

In this paper we make an analysis of KOSPI 200 index options listed in Korea Stock and Futures Exchange whose trading volume is world best these days. We adopt the stochastic volatility model suggested by Heston (1993) for the dynamics of the underlying asset and use EMM to estimate the parameters of option pricing kernel. The SNP distribution of the implied volatility contains AR (2) and ARCH effects, and the skewness of the distribution is much higher than normal distribution. The distribution has thinner left tail and fatter right tail than normal distribution, which is opposite to the case of S&P 500 options market. The result of estimation shows that Implied volatility series of KOSPI 200 options have weak mean reverting property and are almost nonstationary. The correlation coefficient between the implied volatility and returns is estimated to have negligible negative number. These features are also opposite to the case of S&P 500 options market where implied volatility is reported to have strong mean reversion, and the correlation between the implied VIatilIty and retturns is reported to have large negative number.

GENERALIZED BN–S STOCHASTIC VOLATILITY MODEL FOR OPTION PRICING

2016 ◽  
Vol 19 (02) ◽  
pp. 1650014 ◽  
Author(s):  
INDRANIL SENGUPTA
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Gaussian Distribution ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Inverse Gaussian ◽  
Martingale Measures ◽  
Structure Preserving ◽  
Volatility Model ◽  
Equivalent Martingale

In this paper, a class of generalized Barndorff-Nielsen and Shephard (BN–S) models is investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets is studied in terms of equivalent martingale measures (EMM). Variance process is studied in details for the case of Inverse-Gaussian distribution. Various structure preserving subclasses of EMMs are derived. The model is then effectively used for pricing European style options and fitting implied volatility smiles.

scholarly journals MULTISCALE STOCHASTIC VOLATILITY MODEL FOR DERIVATIVES ON FUTURES

2014 ◽  
Vol 17 (07) ◽  
pp. 1450043 ◽  
Author(s):  
JEAN-PIERRE FOUQUE ◽  
YURI F. SAPORITO ◽  
JORGE P. ZUBELLI
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Additional Hypothesis ◽  
First Order ◽  
Volatility Model ◽  
First Order Approximation

In this paper, we present a new method for computing the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility studied in Fouque et al. (2011). It provides an alternative method to the singular perturbation technique presented in Hikspoors & Jaimungal (2008). The main features of our method are twofold: firstly, it does not rely on any additional hypothesis on the regularity of the payoff function, and secondly, it allows an effective and straightforward calibration procedure of the group market parameters to implied volatilities. These features were not achieved in previous works. Moreover, the central argument of our method could be applied to interest rate derivatives and compound derivatives. The only pre-requisite of our approach is the first-order approximation of the underlying derivative. Furthermore, the model proposed here is well-suited for commodities since it incorporates mean reversion of the spot price and multiscale stochastic volatility. Indeed, the model was validated by calibrating the group market parameters to options on crude-oil futures, and it displays a very good fit of the implied volatility.

ON PRICING CONTINGENT CLAIMS UNDER THE DOUBLE HESTON MODEL

2012 ◽  
Vol 15 (05) ◽  
pp. 1250033 ◽  
Author(s):  
M. COSTABILE ◽  
I. MASSABÒ ◽  
E. RUSSO
Keyword(s):  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Contingent Claims ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Underlying Asset ◽  
State Variable ◽  
Proposed Model ◽  
Volatility Model ◽  
Asset Value

This article presents a lattice based approach for pricing contingent claims when the underlying asset evolves according to the double Heston (dH) stochastic volatility model introduced by Christoffersen et al. (2009). We discretize the continuous evolution of both squared volatilities by a "binomial pyramid", and consider the asset value as an auxiliary state variable for which a subset of possible realizations is attached to each node of the pyramid. The elements of the subset cover the range of asset prices at each time slice, and claim price is computed solving backward through the "binomial pyramid". Numerical experiments confirm the accuracy and efficiency of the proposed model.

CURRENCY DERIVATIVES UNDER A MINIMAL MARKET MODEL WITH RANDOM SCALING

2005 ◽  
Vol 08 (08) ◽  
pp. 1157-1177 ◽  
Author(s):  
DAVID HEATH ◽  
ECKHARD PLATEN
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
European Options ◽  
Bessel Processes ◽  
Exchange Rate Dynamics ◽  
Volatility Model ◽  
Minimal Market Model ◽  
Implied Volatility Surfaces

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.

scholarly journals From characteristic functions to implied volatility expansions

2015 ◽  
Vol 47 (03) ◽  
pp. 837-857 ◽  
Author(s):  
Antoine Jacquier ◽  
Matthew Lorig
Keyword(s):  
Characteristic Function ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Volatility Smile ◽  
Model Free ◽  
Implied Volatility Surface ◽  
Volatility Model ◽  
Volatility Surface

For any strictly positive martingaleS= eXfor whichXhas a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log-strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model, Merton (1976), one infinite activity exponential Lévy model (variance gamma), and one stochastic volatility model, Heston (1993). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.

scholarly journals ESTIMASI VALUE AT RISK MENGGUNAKAN VOLATILITAS DISPLACED DIFFUSION

2019 ◽  
Vol 8 (4) ◽  
pp. 298
Author(s):  
MIRANDA NOVI MARA DEWI ◽  
KOMANG DHARMAWAN ◽  
KARTIKA SARI
Keyword(s):  
At Risk ◽  
Stochastic Process ◽  
Stochastic Volatility ◽  
Diffusion Model ◽  
Stock Prices ◽  
Value At Risk ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Financial Asset ◽  
Volatility Model

Value at Risk (VaR) is a measure of risk that is able to calculate the worst possible loss that can occurs to stock prices with a certain level of confidence and within a certain period of time. The purpose of this study was to determine the VaR estimate from PT. Indonesian Telecommunications by using Displaced Diffusion volatility. The Displaced Diffusion Model is a stochastic volatility model that describes changes in a financial asset assuming volatility is not constant, but follows a stochastic process. Displaced Diffusion model are capable of modelling skewed implied volatility structures and frequently applied by interest rate quants. Based on the estimation of Displaced Diffusion volatility, it is found that volatility for PT. Indonesian Telecommunications is 0.010168 and VaR estimation using Displaced Diffusion volatility with a confidence level of  95 percent of 1.63%.

STOCHASTIC VOLATILITY AND JUMP-DIFFUSION — IMPLICATIONS ON OPTION PRICING

1999 ◽  
Vol 02 (04) ◽  
pp. 409-440 ◽  
Author(s):  
GEORGE J. JIANG
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Dynamic Properties ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
Pricing Errors ◽  
Volatility Model ◽  
Random Jump

This paper conducts a thorough and detailed investigation on the implications of stochastic volatility and random jump on option prices. Both stochastic volatility and jump-diffusion processes admit asymmetric and fat-tailed distribution of asset returns and thus have similar impact on option prices compared to the Black–Scholes model. While the dynamic properties of stochastic volatility model are shown to have more impact on long-term options, the random jump is shown to have relatively larger impact on short-term near-the-money options. The misspecification risk of stochastic volatility as jump is minimal in terms of option pricing errors only when both the level of kurtosis of the underlying asset return distribution and the level of volatility persistence are low. While both asymmetric volatility and asymmetric jump can induce distortion of option pricing errors, the skewness of jump offers better explanations to empirical findings on implied volatility curves.

FROM THE IMPLIED VOLATILITY SKEW TO A ROBUST CORRECTION TO BLACK-SCHOLES AMERICAN OPTION PRICES

2001 ◽  
Vol 04 (04) ◽  
pp. 651-675 ◽  
Author(s):  
JEAN-PIERRE FOUQUE ◽  
GEORGE PAPANICOLAOU ◽  
K. RONNIE SIRCAR
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Stochastic Volatility ◽  
Free Boundary Problem ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
One Dimensional ◽  
Volatility Model ◽  
Black Scholes

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of a fixed boundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

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