Related papers: Normalization for Implied Volatility
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
Presented is intuitive proof of Black-Scholes formula for European call options, which is based on arbitrage and properties of lognormal distribution. Paper can help students and non-mathematicians to better understand economic concepts…
This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely…
This work studies the valuation of currency options in markets suffering from a financial crisis. We consider a European option where the underlying asset is a foreign currency. We assume that the value of the underlying asset is a…
In this article we focus on the pricing of exchange options when the dynamic of logprices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al [19]. In particular, for the former…
In this paper, we model financial markets with semi-Markov volatilities and price covarinace and correlation swaps for this markets. Numerical evaluations of vari- nace, volatility, covarinace and correlations swaps with semi-Markov…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $\sigma$, in which the last is defined by a stochastic differential equation with an…
We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical It\^o calculus and Taylor…
We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approximate the total implied variance as a function of…
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…
Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which…
We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks…
The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts {(LETFs)}. We study the relationship between the ETF and LETF implied volatility surfaces when…