Results 1  10
of
16
Asymptotic formulas with error estimates for call pricing functions and the implied volatility at extreme strikes
, 2009
"... In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas for the implied volatility and the tailwing formulas due to Benaim and Friz. In addition, we analyze ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
(Show Context)
In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas for the implied volatility and the tailwing formulas due to Benaim and Friz. In addition, we analyze Paretotype tails of stock price distributions in uncorrelated HullWhite, SteinStein, and Heston models and find asymptotic formulas with error estimates for call pricing functions in these models.
Marginal density expansions for diffusions and stochastic volatility, part I: Theoretical Foundations
 Communications on Pure and Applied Mathematics
"... ar ..."
(Show Context)
Arbitragefree SVI volatility surfaces
 Quantitative Finance
"... In this article, we show how to calibrate the widelyused SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitragefree SVI volatility surfaces with a simple closedform representation. We ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
(Show Context)
In this article, we show how to calibrate the widelyused SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitragefree SVI volatility surfaces with a simple closedform representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data. 1
Shapes of implied volatility with positive mass at zero. arXiv:1310.1020 [qfin.PR
, 2013
"... ar ..."
(Show Context)
On refined volatility smile expansion in the Heston
, 2010
"... It is known that Heston’s stochastic volatility model exhibits moment explosion, and that the critical moment s ∗ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: σBS(k,T) 2 T ∼ Ψ(s ∗ − 1) × k (Roger Lee’ ..."
Abstract
 Add to MetaCart
It is known that Heston’s stochastic volatility model exhibits moment explosion, and that the critical moment s ∗ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: σBS(k,T) 2 T ∼ Ψ(s ∗ − 1) × k (Roger Lee’s moment formula). Motivated by recent “tailwing ” refinements ofthis momentformula, we firstderive anoveltail expansionfor the Heston density, sharpening previous work of Drăgulescu and Yakovenko [Quant. Finance 2, 6 (2002), 443–453], and then show the validity of a refined expansion of the type σBS(k,T) 2 T = (β1k 1/2 +β2 +...) 2, where all constants are explicitly known as functions of s ∗ , the Heston model parameters, spot vol and maturity T. In the case of the “zerocorrelation” Heston model such an expansion was derived by Gulisashvili and Stein [Appl. Math. Opt., DOI: 10.1007/s002450099085]. Our methods and results may prove useful beyond the Heston model: the entire quantitative analysis is based on affine principles; at no point do we need knowledge of the (explicit, but cumbersome) closed form expression of the Fourier transform of logST (equivalently: Mellin transform of ST). Secondly, our analysis reveals a new parameter (“critical slope”), defined in a model free manner, which drives the second and higher order terms in tail and implied volatility expansions. 1
FROM MOMENT EXPLOSION TO THE ASYMPTOTIC BEHAVIOR OF THE CUMULATIVE DISTRIBUTION FOR A RANDOM VARIABLE
, 2013
"... Abstract. We study the Tauberian relations between the moment generating function (MGF) and the complementary cumulative distribution function of a variable whose MGF is finite only on part of the real line. We relate the right tail behavior of the cumulative distribution function of such a random v ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We study the Tauberian relations between the moment generating function (MGF) and the complementary cumulative distribution function of a variable whose MGF is finite only on part of the real line. We relate the right tail behavior of the cumulative distribution function of such a random variable to the behavior of its MGF near the critical moment. We apply our results to an arbitrary superposition of a CIR process and the timeintegral of this process.