Entropy Concepts Applied to Option Pricing

Uncertainty is one of the most important concept in financial mathematics applications. In this paper we review some important aspects related to the application of entropy-related concepts to option pricing. The Kullback-Leibler information divergence and the informational energy introduced by Onicescu are the main tools investigated in this paper. We highlight a necessary condition that must be verified when obtaining the probability distribution minimising the Kullback-Leibler information divergence. Deriving a probability distribution by optimising the information energy has some pitfalls that are discussed in this paper

Estimation functions and uniformly most powerful tests for inverse Gaussian distribution

summary:The aim of this article is to develop estimation functions by confidence regions for the inverse Gaussian distribution with two parameters and to construct tests for hypotheses testing concerning the parameter $\lambda$ when the mean parameter $\mu$ is known. The tests constructed are uniformly most powerful tests and for testing the point null hypothesis it is also unbiased

A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches

A factor model is proposed for the valuation of credit default swaps, credit indices and CDO contracts. The model of default is based on the first-passage distribution of a Brownian motion time modified by a continuous time-change. Various model specifications fall under this general approach based on defining the credit-quality process as an innovative time-change of a standard Brownian motion where the volatility process is mean reverting Lévy driven OU type process. Our models are bottom-up and can account for sudden moves in the level of CDS spreads representing the so-called credit gap risk. We develop FFT computational tools for calculating the distribution of losses and we show how to apply them to several specifications of the time-changed Brownian motion. Our line of modelling is flexible enough to facilitate the derivation of analytical formulae for conditional probabilities of default and prices of credit derivatives

Options-based systemic risk, financial distress, and macroeconomic downturns

In this study, we propose an implied forward-looking measure for systemic risk that employs the information from put option prices, the Systemic Options Value-at-Risk (SOVaR). This new measure can capture the buildup stage of systemic risk in the financial sector earlier than the standard stock market-based systemic risk measures (SRMs). Non-parametric tests show that our measure exhibits more timely early warning signals (up to one month earlier) regarding the main turbulent events around the global financial crisis of 2007-2009 than the three main stock market-based SRMs. Moreover, this new measure also shows significant predictive power with respect to macroeconomic downturns as well as future recessions. Our results are robust to various specifications, breakdowns of financial sectors, and controlling for the other main risk measures proposed in the literature

Asymmetric network connectedness of fears

This paper introduces forward-looking measures of the network connectedness of fears in the financial system, arising due to the good and bad beliefs of market participants about uncertainty that spreads unequally across a network of banks. We argue that this asymmetric network structure extracted from call and put traded option prices of the main U.S. banks contains valuable information for predicting macroeconomic conditions and economic uncertainty, and it can serve as a tool for forward-looking systemic risk monitoring