Related papers: The Chebyshev method for the implied volatility

It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…

We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original…

Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a…

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…

Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has…

A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…

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…

For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…

The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in $\C^d.$ We study this problem on general sets, but devote special attention to product sets…

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…

We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we…

We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…

We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new…

We apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of…

We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis…

In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…

First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time-value of a European call option. Then, we formulate an…