Bilateral Gamma processes generalize the Variance Gamma process and allow to capture more precisely the differences between upward and downward moves of financial returns, notably in terms of jump speed, frequency, and size. Like in most other pure jump models, option pricing under Bilateral...

Compound options are options for which the underlying is another option. In other words, a compound option is an option written on an option. In this paper, we present two new approaches to compound option pricing. The first approach relies on Malliavin calculus methods and the Clark-Ocone...

To value non-transferable non-hedgeable (NTNH) contingent claims and price executive stock options (ESOs), we use a replication argument to translate portfolios with NTNH derivatives into portfolios of primary assets (only) with stochastic portfolio constraints. By identifying stochastic...

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary...

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept `reciprocity'. The argument is based on identifying an equivalence between the contemporary, and ostensibly 'value neutral', Fundamental Theory of Asset Pricing with...

Many efficient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the...

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan (1998), extends to "standard dispersion" options written on the Euclidean norm of a vector of n asset performances. With the help of...

We consider the filtering model of Frey & Schmidt (2012) stated under the real probability measure and develop a method for estimating the parameters in this framework by using time-series data of CDS index spreads and classical maximum-likelihood algorithms. The estimation-approach incorporates...

In this paper we give a new proof to the Engelbert-Schmidt zero-one law for time-homogeneous diffusions, which provides deterministic criteria for the convergence of integral functional of diffusions. Our proof is based on stochastic time change and Feller's test of explosions, and does not rely...

Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi c and Urusov (2012c) give necessary and sufficient conditions in the case of...