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On dependence of the implied volatility on returns for stochastic volatility models
stochastic volatility the Heston model
2010/10/21
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model.To be more specific, we consider the conditional expectation of vari...
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given...
Asymptotic formulae for implied volatility in the Heston model
Asymptotic formulae implied volatility Heston model
2010/11/2
In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in t...
Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models
true martingales one-dimensional diffusions separating times financial bubbles
2010/11/1
The stochastic exponential Zt = exp{Mt − M0 − (1/2)hM,Mit} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the ...