We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied...

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied...

We provide a simple and explicit construction of a family of stochastic exponentials with expectation k$/in$(0,1). Our family of stochastic exponentials can be constructed to be either strictly positive of merely non-negative

The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this...

In this paper we study a class of infinite horizon fully coupled forward-backward stochastic differential equations (FBSDEs), that are stimulated by various continuous time future expectations models with random coefficients. Under standard Lipschitz and monotonicity conditions, and by means of...

The proliferation of algorithmic high-frequency trading in financial markets has also led to an increase in new types of fraudulent activity. Since the flash-crash of 2010 first brought it to popular prominence, layering or spoofing fraud has become a major concern for financial regulators...

This paper provides the proofs to the analysis of a continuous time matching model with saving in Bayer and Wälde (2010a). The paper proves the results on consumption growth, provides an existence proof for optimal consumption and a detailed derivation of the Fokker-Planck equations

In this study we propose a stochastic mortality forecast model that may be viewed as a Lévy process. First, age, period and cohort effects are objectively identified in a given matrix of historic mortality data. Next, these patterns are removed from the matrix of mortality improvement rates. We...

This paper discusses the relation between forward price models (FPM) and the so called implied volatility term structure (VTS). We start by considering the case of pure deterministic forward price volatilities and suppose both forward contracts and at-the-money (ATM) options, on a same...