Related papers: Volatility in options formulae for general stochas…
Time variation and persistence are crucial properties of volatility that are often studied separately in energy volatility forecasting models. Here, we propose a novel approach that allows shocks with heterogeneous persistence to vary…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
The Black-Scholes model anticipates rather well the observed prices for options in the case of a strike price that is not too far from the current price of the underlying asset. Some useful extensions can be obtained by an adequate…
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…
A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The…
Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the…
We study general properties such as the solution representation of a moving boundary value problem of the Black-Scholes equation, its min-max estimation, lower and upper gradient estimates, and strict monotonicity with respect to the…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…
This paper studies the model risk of the Black-Scholes (BS) model in pricing and risk-managing variable annuities motivated by its wide usage in the insurance industry. Specifically, we derive a model-free decomposition of the no-arbitrage…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in…
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…
It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
Employing the Klein-Gordon equation, we propose a generalized Black-Scholes equation. In addition, we found a limit where this generalized equation is invariant under conformal transformations, in particular invariant under scale…
Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long…
This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…