International Journal of Theoretical and Applied Finance

In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at ) for perpetual American options when the Call-Put payoff (y - x)⁺ is replaced by ϕ(x,y). It turns out that the duality still holds under monotonicity and concavity assumptions on ϕ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for European options. Last, we give some examples for which the optimal strategy is known explicitly.

We propose a decomposition of financial time series into Gaussian subsequences characterized by a constant Hölder exponent. In (multi)fractal models this condition is equivalent to the subsequences themselves being stationarity. For the different subsequences, we study the scaling of the variance and the bias that is generated when the Hölder exponent is re-estimated using traditional estimators. The results achieved by both analyses are shown to be strongly consistent with the assumption that the price process can be modeled by the multifractional Brownian motion, a nonstationary process whose Hölder regularity changes from point to point.

We obtain lower and upper bounds on option prices in one-dimensional jump-diffusion markets with point process components. Our proofs rely in general on the classical Kolmogorov equation argument and on the propagation of convexity property for Markov semigroups, but the bounds on intensities and jump sizes formulated in our hypotheses are different from the ones already found in the literature (Finance and Stochastics4(2) (2000) 209–222; 10(2) (2006) 229–249).

We consider reduced-form models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modeled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be modeled explicitly. In the present paper this class of models is analyzed by Markov process techniques. We study in detail the pricing and the hedging of portfolio-related credit derivatives such as basket default swaps and collaterized debt obligations (CDOs) and discuss the calibration to market data.

In this paper we present a prepayment-risk-neutral valuation model for fixed-rate Mortgage-Backed Securities. Our model is based on intensity models as used in credit-risk modeling and extends existing models for individual mortgage contracts in a proportional hazard framework. The general economic environment is explicitly accounted for in the prepayment process by an additional factor which we fit to the quarterly GDP growth rate in the US. In our risk-neutral setting we account for both the fears of refinancing understatement and turnover overstatement which sometimes result in higher option-adjusted spreads (OAS) for premiums and discounts respectively. We apply our prepayment-risk-neutral pricing approach to a sample of generic 30yr GNMA MBS pass-throughs from 1996 to 2006. Our empirical results indicate that the GDP growth factor adds explanatory power to the model.