8 papers
The It{ô}-Föllmer formula -- nonstandard cases
W. M. Bednorz, R. M. Łochowski, P. L. Zondi +2
The purpose of this note is to prove the It{ô}-Föllmer formula for the càdlàg paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions…
Sensitivity analysis of path-dependent options in an incomplete market with pathwise functional Ito calculus
Siboniso Confrence Nkosi, Farai Julius Mhlanga
Functional It^o calculus is based on an extension of the classical It^o calculus to functionals depending on the entire past evolution of the underlying paths and not only on its c…
Quadratic variation and local times of the horizontal component of the Peano curve (square filling curve)
Phumlani L. Zondi, Darlington Hove, Rafał M. Łochowski +1
We show that the horizontal component of the Peano curve has quadratic variation equal the limit of quadratic variations along the Lebesgue partitions for grids of the form $3^{-n}…
Local times of deterministic paths with finite variation
Darlington Hove, Farai J. Mhlanga, Rafał M. Łochowski +1
In this note, we define the numbers of level crossings by a c{à}dl{à}g (RCLL) real function and, in analogy to the work of Bertoin and Yor [BY14] we…
On the sensitivity analysis of spread options using Malliavin calculus
Farai Julius Mhlanga, Shadrack Makwena Kgomo
In this paper we derive tractable formulae for price sensitivities of two-dimensional spread options using Malliavin calculus. In particular, we consider spread options with asset…
On the sensitivity analysis of energy quanto options
Rodwell Kufakunesu, Farai Mhlanga
In recent years there has been an advent of quanto options in energy markets. The structure of the payoff is rather a different type from other markets since it is written as a pro…