Related papers: Asymptotics of forward implied volatility
We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with…
In this note, we derive the characteristic function expansion for logarithm of the underlying asset price in corrected Heston model as proposed by Fouque and Lorig.
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…
In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used…
The analysis of observed conditional distributions of both lagged and simultaneous intraday price increments of a basket of stocks reveals phenomena of dependence - induced volatility smile and kurtosis reduction. A model based on…
A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends on the value of the return. The solution…
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],…
Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution…
How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as…
Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for…
We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first…
We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…
In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders.…
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the…
We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the…
In this study, we constructed daily high-frequency sentiment data and used the VAR method to attempt to predict the next day's implied volatility surface. We utilized 630,000 text data entries from the East Money Stock Forum from 2014 to…
We consider the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant…
In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus…
We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in…