Related papers: The Small-Maturity Heston Forward Smile

Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the Constant Elasticity of Variance (CEV) model. We present an analytical…

We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous…

We provide explicit approximation formulas for VIX futures and options in forward variance models, with particular emphasis on the family of so-called Bergomi models: the one-factor Bergomi model [Bergomi, Smile dynamics II, Risk, 2005],…

We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention…

This paper proposes a Monte Carlo technique for pricing the forward yield to maturity, when the volatility of the zero-coupon bond is known. We make the assumption of deterministic default intensity (Hazard Rate Function). We make no…

We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an It\^o semimartingale over a shrinking time interval. The spot characteristics of the It\^o semimartingale are allowed to have…

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…

We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility…

It is well know that, in the short maturity limit, the implied volatility approaches the integral harmonic mean of the local volatility with respect to log-strike, see [Berestycki et al., Asymptotics and calibration of local volatility…

Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able…

The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the…

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At…

Particles labelled $1,...,n$ are initially arranged in increasing order. Subsequently, each pair of neighboring particles that is currently in increasing order swaps according to a Poisson process of rate 1. We analyze the asymptotic…

We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a…

We consider the Heath-Jarrow-Morton model of forward rates processes with linear volatility. The noise is either a Wiener or a pure jump Leevy process. We provide formulae for the forward rate processes, and discus the problem of their…

We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the…

In the present paper, a decomposition formula for the call price due to Al\`{o}s is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the…

We study the asymptotic behavior of small deviation probabilities for the critical Galton-Watson processes with infinite variance of the offspring sizes of particles and apply the obtained result to investigate the structure of a reduced…