scholarly journals Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2038
Author(s):  
Petra Posedel Šimović ◽  
Azra Tafro
Keyword(s):  
Risk Premium ◽  
Transition Probabilities ◽  
Market Price ◽  
Stochastic Volatility Model ◽  
Volatility Risk ◽  
Underlying Asset ◽  
Asset Return ◽  
Volatility Model ◽  
Local Risk ◽  
Market Shocks

Investors’ decisions on capital markets depend on their anticipation and preferences about risk, and volatility is one of the most common measures of risk. This paper proposes a method of estimating the market price of volatility risk by incorporating both conditional heteroscedasticity and nonlinear effects in market returns, while accounting for asymmetric shocks. We develop a model that allows dynamic risk premiums for the underlying asset and for the volatility of the asset under the physical measure. Specifically, a nonlinear in mean time series model combining the asymmetric autoregressive conditional heteroscedastic model with leverage (NGARCH) is adapted for modeling return dynamics. The local risk-neutral valuation relationship is used to model investors’ preferences of volatility risk. The transition probabilities governing the evolution of the price of the underlying asset are adjusted for investors’ attitude towards risk, presenting the asset returns as a function of the risk premium. Numerical studies on asset return data show the significance of market shocks and levels of asymmetry in pricing the volatility risk. Estimated premiums could be used in option pricing models, turning options markets into volatility trading markets, and in measuring reactions to market shocks.

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.

MODELING AND SIMULATION OF SEQUENTIAL AUCTIONS: PRICING AND CALIBRATION ALGORITHMS

2012 ◽  
Vol 03 (03) ◽  
pp. 1250009 ◽  
Author(s):  
EMMANUEL M. TADJOUDDINE
Keyword(s):  
Market Price ◽  
Payoff Function ◽  
Stochastic Volatility Model ◽  
Sequential Auctions ◽  
Future Market ◽  
Market Data ◽  
Algorithmic Differentiation ◽  
Financial Products ◽  
Volatility Model ◽  
The Right

We consider sequential auctions wherein seller and bidder agents need to price goods on sale at the 'right' market price. We propose algorithms based on a binomial model for both the seller and buyer. Then, we consider the problem of calibrating pricing models to market data. To this end, we studied a stochastic volatility model used for option pricing, derived, and analyzed Monte Carlo estimators for computing the gradient of a certain payoff function using Finite Differencing and Algorithmic Differentiation. We then assessed the accuracy and efficiency of both methods as well as their impacts into the optimization algorithm. Numerical results are presented and discussed. This work can benefit those engaged in electronic trading or investors in financial products with the need for fast and more precise predictions of future market data.

scholarly journals European Option Pricing under Wishart Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Raphael Naryongo ◽  
Philip Ngare ◽  
Anthony Waititu
Keyword(s):  
Option Pricing ◽  
Market Price ◽  
Stochastic Volatility Model ◽  
European Option ◽  
Multifactor Model ◽  
Asset Pricing Model ◽  
European Option Pricing ◽  
Volatility Model ◽  
Wishart Processes ◽  
The Fourier Transform

This study deals with a single risky asset pricing model whose volatility is described by Wishart affine processes. This multifactor model with two dependency matrices describing the correlation between the asset dynamic and Wishart processes makes it more flexible enough to fit the market data for short or long maturities. The aim of the study is to derive and solve the call option pricing problem under the double Wishart stochastic volatility model. The Fourier transform techniques combined with perturbation methods are employed in order to price the European call options. The numerical illustrations on pricing predictions show similar behavior of price movements under the double Wishart model with respect to the market price.

scholarly journals The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Raphael Naryongo ◽  
Philip Ngare ◽  
Anthony Waititu
Keyword(s):  
Diffusion Processes ◽  
Asset Returns ◽  
Stochastic Volatility Model ◽  
Model Parameters ◽  
Market Prices ◽  
Asset Return ◽  
Volatility Model ◽  
Squared Bessel Process ◽  
Wishart Processes ◽  
Discretization Technique

This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.

scholarly journals Pricing Collar Options with Stochastic Volatility

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Pengshi Li ◽  
Jianhui Yang
Keyword(s):  
Brownian Motion ◽  
Numerical Experiment ◽  
Stochastic Volatility ◽  
Asset Price ◽  
Analytical Approximation ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Underlying Asset ◽  
Volatility Model ◽  
Mean Reverting Process

This paper studies collar options in a stochastic volatility economy. The underlying asset price is assumed to follow a continuous geometric Brownian motion with stochastic volatility driven by a mean-reverting process. The method of asymptotic analysis is employed to solve the PDE in the stochastic volatility model. An analytical approximation formula for the price of the collar option is derived. A numerical experiment is presented to demonstrate the results.

A Study on the Return Dynamics using the Implied Information

2007 ◽  
Vol 15 (2) ◽  
pp. 55-83
Author(s):  
Moo Sung Kim ◽  
Tae Hun Kang
Keyword(s):  
Risk Premium ◽  
Asset Price ◽  
Stock Index ◽  
Index Options ◽  
Volatility Risk ◽  
Underlying Asset ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Option Model ◽  
Return Dynamics

This article empirically analyzes some properties by all one-dimensional diffusion option models by using the martingale restriction test and examines the systematic risk factors Implied In return dynamics of KOSPI 200 index options. We find that the martingale restriction under one-dimensional diffusion option model is strongly rejected by the data because of the negative volatility risk premium. Therefore options are not redundant securities, nor monotonically increasing (decreasing) in the underlying asset price and also option prices are not perfectly correlated with each other and with the underlying asset. And under the non-complete of the market. the informational led-lag relationship between the stock indices and the stock index options exist.

scholarly journals Effect of Variance Swap in Hedging Volatility Risk

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 70
Author(s):  
Yang Shen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Volatility Model ◽  
Linear Quadratic ◽  
Bank Account ◽  
Volatility Risk ◽  
Variance Swap ◽  
Volatility Model ◽  
Mean Variance

This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We consider two mean-variance portfolio selection problems under Heston’s stochastic volatility model. In the first problem, the financial market is complete and contains three primitive assets: a bank account, a stock and a variance swap, where the variance swap can be used to hedge against the volatility risk. In the second problem, only the bank account and the stock can be traded in the market, which is incomplete since the idiosyncratic volatility risk is unhedgeable. Under an exponential integrability assumption, we use a linear-quadratic control approach in conjunction with backward stochastic differential equations to solve the two problems. Efficient portfolio strategies and efficient frontiers are derived in closed-form and represented in terms of the unique solutions to backward stochastic differential equations. Numerical examples are provided to compare the solutions to the two problems. It is found that adding the variance swap in the portfolio can remarkably reduce the portfolio risk.

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.

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