Narrow Results

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. In this paper I further test the truncated Levy paradigm using high frequency data from the Australian All Ordinaries share market index. I then consider an optimal option hedging strategy which is appropriate for the early Levy dominated regime. This is compared with the usual delta hedging approach and found to differ significantly.

This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipović, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional Lévy process. The contribution of this work is twofold: we provide conditions for absence of arbitrage in this generalized framework. Furthermore, we study the relation to market models by embedding them in the forward rate framework in spirit of Brace, Gatarek and Musiela (1997).

In this paper a stochastic volatility model is considered. That is, a log price process Y which is given in terms of a volatility process V is studied. The latter is defined such that the log price possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang^[6]. In the model there are two sets of unknown parameters, one set corresponding to the marginal distribution of V and one to autocorrelation of V. Based on discrete time observations of the log price the authors discuss how to estimate the parameters appearing in the marginal distribution and find the asymptotic properties.

Using a real option approach, this paper models an arbitrary real life investment, which typically has a long maturity date, as a perpetual American call option in a Levy market. Expressions for the moments, characteristic function and infinitesimal generator of the associated jump-diffusion Levy process, defined by two independent compound Poisson processes and two correlated standard Brownian motions, are derived and these fundamental results are employed to determine the optimal time for investment. An application of the results to a Build Operate and Transfer investment is furnished.

This chapter studies total positivity and relative convexity properties in option pricing models. We introduce these properties in the Black–Scholes setting by showing the following: out-of-the-money calls are totally positive in strike and volatility, out-of-the-money puts have a reverse sign rule property, calls and puts are convex with respect to at-the-money prices and relative convexity of option prices implies a convexity-in-time property of the underlying. We then extend these properties to other models, including scalar diffusions, mixture models and certain Lévy processes. We show that relative convexity typically holds in time-homogeneous local volatility models through the Dupire equation. We develop implications of these ideas for empirical option prices, including constraints on the at-the-money skew. We illustrate connections with models studied by Peter Carr, including the variance-gamma, CGMY, Dagum and logistic density models.