No arbitrage without semimartingales

We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example, fractional Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/08-AAP554 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A hybrid information approach to predict corporate credit risk

This article proposes a hybrid information approach to predict corporate credit risk. In contrast to the previous literature that debates which credit risk model is the best, we pool information from a diverse set of structural and reduced-form models to produce a model combination based credit risk prediction. Compared with each single model, the pooled strategies yield consistently lower average risk prediction errors over time. We also find that while the reduced-form models contribute more in the pooled strategies for speculative grade names and longer maturities, the structural models have higher weights for shorter maturities and investment grade names

A Common Market Measure for Libor and Pricing Caps, Floors and Swaps in a Field Theory of Forward Interest Rates

The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally for such models. To elaborate how the martingale for the Libor belongs to the general class of numeraire for the forward interest rates, two other numeraire's are considered, namely the money market measure that makes the evolution of the zero coupon bonds a martingale, and the forward measure for which the forward bond price is a martingale. The price of an interest rate cap is computed for all three numeraires, and is shown to be numeraire invariant. Put-call parity is discussed in some detail and shown to emerge due to some non-trivial properties of the numeraires. Some properties of swaps, and their relation to caps and floors, are briefly discussed.Comment: 28 pages, 4 figure

Filtration Reduction and Completeness in Jump-Diffusion Models

This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted to the original economy using the notion of consistency. For pedagogical purposes, we begin with simple setups and progressively extend to models of increasing generality

Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk

This paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk-return frontier and shows that hedging strategies - such as the transfer of longevity risk - may increase the overall risk while decreasing expected returns, thus resulting in inefficient outcomes. Once calibrated to the 2010 UK longevity and bond market, the model gives conditions under which hedging policies become inefficient

Testing Option Pricing with the Edgeworth Expansion

There is a well developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-gaussian distributions. In this contribution we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the brazilian and american markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments.Comment: 9 pages, 3 figure. Contribution to the International Workshop on Trends and Perspectives on Extensive and Non-Extensive Statistical Mechanics, November 19-21, 2003, Angra dos Reis, Brazi