A Multivariate Jump-Driven Financial Asset Model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behavior of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a sto- chastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that - opposite to other, non jointly Gaussian settings - its risk neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.Lévy processes, multivariate asset modelling, copulas, risk neutral dependence.

Self exciting threshold interest rates models.

In this paper, we study a new class of tractable diffusions suitable for model's primitives of interest rates. We consider scalar diffusions with scale s'(x) and speed m(x) densities discontinuous at the level x*. We call that family of processes Self Exciting Threshold (SET) diffusions. Following Gorovoi and Linetsky (2004), we obtain semianalytical expressions for the transition density of SET (killed) diffusions. We propose several applications to interest rates modeling. We show that SET short rate processes do not generate arbitrage possibilities and we adapt the HJM procedure to forward rates with discontinuous scale density. We also extend the CEV and the shiftedlognormal Libor market models. Finally, the models are calibrated to the U.S. market. SET diffusions can also be used to model stock price, stochastic volatility, credit spread, etc.Eigenfunction expansions; Interest rates; Market models; SETAR; Skew Brownian motion; State-price density;

On the suboptimality of path-dependent pay-offs in Lévy markets.

Cox & Leland (2000) use techniques from the field of stochastic control theory to show that in the particular case of a Brownian motion for the asset returns all risk averse decisionmakers with a fixed investment horizon prefer path-independent payoffs over path-dependent ones. We will provide a novel and simple proof for the Cox&Leland result and we will extend it to general, not necessarily complete, Lévymarkets. It is also shown that in these markets optimal path-independent pay-offs have final values increasing with the underlying asset value. Our results imply that path-dependent investment payoffs, the use of which is widespread in financial markets, do not appear to offer good value for risk averse decisionmakers with a fixed investment horizonResearch; Approximation; Distribution; Risk; Risk measure; Lognormal; Random variables; Variables; Lower bounds; Choice; Variance; Goodness of fit; Actuarial; Problems; Framework; Requirements; Credit; Portfolio; Impact; Software; Value; Data; Markets; Market; Field; Control; Control theory; Theory; Brownian motion; Investment; IT; Optimal;

An overview of Portfolio Insurances: CPPI and CPDO

Derivative instruments attempt to protect a portfolio against failure events. Constant proportion portfolio insurance (CPPI) and constant proportion debt obligations (CPDO) strategies are recent innovations and have only been adopted in the credit market for the last couple of years. Since their introduction, CPPI strategies have been popular because they provide protection while at the same time they offer high yields. CPDOs were only introduced into the market in 2006 and can be considered as a variation of the CPPI with as main difference the fact that CPDOs do not provide principal protection. Both CPPI and CPDO strategies take investment positions in a risk-free bond and a risky portfolio (often one or more credit default swaps). At each step, the portfolio is rebalanced and the level of risk taken will depend on the distance between the current value of the portfolio and the necessary amount needed to full all the future obligations. In a first step the functioning of both products is studied in depth concluding with drawing some conclusions on their risky-ness.JRC.G.9-Econometrics and statistical support to antifrau

Backward Stochastic Differential Equations and Feynman-Kac Formula for Lévy Processes, with Applications in Finance

This is the publisher's version, also available electronically from http://www.jstor.org/stable/3318541?origin=crossref&seq=1#page_scan_tab_contents.See article for abstract

Static hedging of Asian options under Lévy models: the comonotonicity approach.

In this paper we present a simple static super-hedging strategy for the payoff of an arithmetic Asian option in terms of a portfolio of European options. Moreover, it is shown that the obtained hedge is optimal in some sense. The strategy is based on stop-loss transforms and is applicable under general stock price models. We focus on some popular Lévy models. Numerical illustrations of the hedging performance are given for various Lévy models calibrated to market data of the S&P 500.Comonotonicity; Data; Hedging; Market; Model; Models; Optimal; Options; Performance; Portfolio; Strategy;

The herd behavior index: A new measure for systemic risk in financial markets.

We introduce a new and easy to calculate measure for systemic risk in financial markets. This measure is baptized the Herd Behavior Index (HIX). It is model-independent and forward looking, based on observed option data. In order to determine the degree of systemic risk or herd behavior in a financial market one should compare the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The Herd Behavior Index (HIX) is defined as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance of this extreme market situation. Using the theory of comonotonicity, the extreme situation can easily be backed out of the observed option quotes. The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days implied Herd Behavior Index for the Dow Jones Industrial Average, covering the period January 2003 to October 2009.Comonotonicity; systemic risk; correlation; VIX volatility index;

FIX - The fear index. Measuring market fear.

In this paper, we propose a new fear index based on (equity) option surfaces of an index and its components. The quanti¯cation of the fear level will be solely based on option price data. The index takes into account market risk via the VIX volatility barometer, liquidity risk via the concept of implied liquidity, and systemic risk and herd-behavior via the concept of comonotonicity. It thus allows us to measure an overall level of fear (excluding credit risk) in the market as well as to identify precisely the individual importance of the distinct risk components (market, liquidity or systemic risk). As a side result we also derive an upperbound for the VIX.