arXiv subjects

Antonis Papapantoleon

Publications and source records attributed to Antonis Papapantoleon.

39 records · Page 3Linked to original sources

arXiv2009

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in Lévy and stochastic volatility models.

q-fin.PR↗

arXiv2009

On the valuation of compositions in Lévy term structure models

We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models for the evolution of interest rates: an HJM-type forward rate model and a LIBOR-type forward price model. Both models are driven by a time-inhomogeneous Lévy process.

q-fin.PR↗

arXiv2008

An introduction to Lévy processes with applications in finance

These lectures notes aim at introducing Lévy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of Lévy processes. We analyze a `toy' example of a Lévy process, viz. a Lévy jump-diffusion, which yet offers significant insight into the distributional and path structure of a Lévy process. Then, we present several important results about Lévy processes, such as infinite divisibility and the Lévy-Khintchine formula, the Lévy-Itô decomposition, the Itô formula for Lévy processes and Girsanov's transformation. Some (sketches of) proofs are presented, still the majority of proofs is omitted and the reader is referred to textbooks instead. In the second part, we turn our attention to the applications of Lévy processes in financial modeling and option pricing. We discuss how the price process of an asset can be modeled using Lévy processes and give a brief account of market incompleteness. Popular models in the literature are presented and revisited from the point of view of Lévy processes, and we also discuss three methods for pricing financial derivatives. Finally, some indicative evidence from applications to market data is presented.

q-fin.PR↗