Related papers: On the Bachelier implied volatility at extreme str…

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…

In a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility {\sigma} and its derivatives with respect to log-strike k and maturity T near expiry and at the money. We recover explicit limits of these…

Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…

In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered…

The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…

This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised.…

In the standard Black-Scholes-Merton framework, dividends are represented as a continuous dividend yield and the pricing of Vanilla options on a stock is achieved through the well-known Black-Scholes formula. In reality however, stocks pay…

We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…

In financial markets, accurately measuring the risk of future fluctuations in asset prices is of paramount importance. Studies such as Carr and Madan have shown that the expected value of the quadratic variation of log prices can be…

The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets…

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…

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 global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV),…

Scaling properties of the BUX index are similar to those observed in other parts of the world. The main difference is that the traditional quantities like volatility, growth and autocorrelation of returns follows more closely the…

We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but…

Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…

We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are…

The Black-Scholes framework is crucial in pricing a vast number of financial instruments that permeate the complex dynamics of world markets. Associated with this framework, we consider a second-order differential operator $L(x,…

In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of…

In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as…