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International Journal of Theoretical and Applied Finance, 2002
Hull and White [1] have priced a European call option for the case in which the volatility of the underlying asset is a lognormally distributed random variable. They have obtained their formula under the assumption of uncorrelated innovations in security price and volatility.
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Hull and White [1] have priced a European call option for the case in which the volatility of the underlying asset is a lognormally distributed random variable. They have obtained their formula under the assumption of uncorrelated innovations in security price and volatility.
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2008
Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time; early commentators include Mandelbrot (1963) and Officer (1973). It was also clear to the founding
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Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic time-varying volatility and codependence found in financial markets. Such dependence has been known for a long time; early commentators include Mandelbrot (1963) and Officer (1973). It was also clear to the founding
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Stochastic Volatility of Volatility and Variance Risk Premia
SSRN Electronic Journal, 2011This article introduces a new class of stochastic volatility models which allows for stochastic volatility of volatility (SVV): Volatility modulated non-Gaussian Ornstein--Uhlenbeck (VMOU) processes. Various probabilistic properties of (integrated) VMOU processes are presented.
Barndorff-nielsen, O.E., Veraart, A.E.D.
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On calibration of stochastic and fractional stochastic volatility models
European Journal of Operational Research, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Milan Mrázek +2 more
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Asset Pricing with Stochastic Volatility
Applied Mathematics & Optimization, 2001Let a market consist of a stock \(S_t\) and a bond \(B_t\) governed by the equations \[ dS_t= a(t,S_t)S_tdt+ \sigma_tS_tdw_t \] and \[ dB_t=r_t B_tdt,\;B_0=1, \] where \(r_t\) is a bounded, nonnegative, progressively measurable interest rate process. The volatility \(\sigma_t\) is supposed to be random and satisfying on another stochastic differential ...
Kallianpur, G., Xiong, J.
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Discrete Stochastic Autoregressive Volatility
SSRN Electronic Journal, 2013Abstract We use Markov chain methods to develop a flexible class of discrete stochastic autoregressive volatility (DSARV) models. Our approach to formulating the models is straightforward, and readily accommodates features such as volatility asymmetry and time-varying volatility persistence.
Adriana S. Cordis, Chris Kirby
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Complete Models with Stochastic Volatility
Mathematical Finance, 1998The paper proposes an original class of models for the continuous‐time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log‐price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process ...
Hobson, David G., Rogers, L. C. G.
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IMPLIED AND LOCAL VOLATILITIES UNDER STOCHASTIC VOLATILITY
International Journal of Theoretical and Applied Finance, 2001For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process.
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