The risky assets prices of the bi-variate model are reviewed under the hegemonize concentration filtered physical probability space. In the stochastic variance of the Cox-Ingersoll-Ross process. The Mean-variance hedging expanse on the Föllmer-Schweizer decomposition is stringent to the...

This note discusses the impact of dividend modelling on the pricing of equity exotic derivatives under a local volatility model. It explains how the level of the implied local variance is adjusted as the contribution of proportional dividends is increased and characterises the impact of the...

Vanna-volga is a popular method for interpolation/extrapolation of volatility smiles. The technique is widely used in the FX markets context, due to its ability to consistently construct the entire lognormal smile using only three lognormal market quotes.However, the derivation of vanna-volga...

Stochastic volatility models have grown in popularity in the past decade or two. However, for many stochastic volatility models, the functional form of volatility along with the description of the diffusion process for volatility have been posed with analytic convenience in mind. Here, we...

The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....

Reformulating the results of del Baño Rollin, Ferreiro-Castilla, and Utzet (2010), we are able to give necessary and sufficient conditions for the moments of the stock price to exist and extend Theorem 2.1 of Forde and Jacquier (2011). Precisely Forde and Jacquier (2011) provide necessary...

We propose to use the transformed densities introduced in [1] to parametrise volatility smiles. We derive closed form formulas for European options to allow for an effective computation of implied volatilities

In this paper, we derive optimal hedging strategies for options in electricity futures markets. Optimality is measured in terms of minimal variance and the associated minimal variance hedging portfolios are obtained by a stochastic maximum principle. Our explicit results are particularly useful...

The number of crossings of the implied volatility function with a fixed level is bounded above by the number of crossings of the risk-neutral density with the density of a log-normal distribution with the same mean as the forward price. It is bounded below by the number of convex payoffs priced...