We consider the problem of estimating the fractional order of a Lévy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two...

We argue that Islamic principles, in particular the avoidance of ribā and gharar should be applied with respect to real economic value rather than to monetary value in terms of conventional currency. In order to reconcile monetary value with economic value, we propose a reference currency...

Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic...

An analogue can be made between: (a) the slow pace at which species adapt to an environment, which often results in the emergence of a new distinct species out of a once homogeneous genetic pool, and (b) the slow changes that take place over time within a fund, mutating its investment style. A...

Every density produced by an SDE which employs normal random variables for its simulation is either linear or non-linear transformation of the normal random variables. We find this transformation in case of a general SDE by taking into account how the variance evolves in that certain SDE. We map...

In this paper we consider the object oriented implementation of numerical algorithms where arithmetic operators (add, mult, exp) operate on objects with more complex structure (compared to floating point numbers). Examples are objects representing vectors instead of scalars, random variables,...

We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the...