arXiv · arXiv · 2026
Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recov…
Pere Diaz-Lozano, Thomas K. Kloster
arXiv · arXiv · 2023
This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy.But these methods cannot integrate transaction costs or become computationally heavy and hardly applicable. In this paper, we try to tackle this allocation problem by proposing an innovative approach which relies o…
Areski Cousin, Jérôme Lelong, Tom Picard
arXiv · arXiv · 2019
In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, in which we basically replace the standard least square regression by a Wiener chaos expansion. Not only does it allow us to deal with a non Markovian setting, b…
Jérôme Lelong
arXiv · arXiv · 2016
We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is that it relies only on an integrability condition.
Kristoffer Lindensjö
arXiv · arXiv · 2013
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpreta…
Christian Bayer, Peter K. Friz
arXiv · arXiv · 2011
In the setting proposed by Hughston & Rafailidis (2005) we consider general interest rate models in the case of a Brownian market information filtration $(\mathcal{F}_t)_{t\geq0}$. Let $X$ be a square-integrable $\mathcal{F}_\infty$-measurable random variable, and assume the non-degeneracy condition that for all $t<\infty$ the random variable $X$ is not $\mathcal{F}_t$-measurable. Let ${σ_t}$ denote the integrand app…
Lane P. Hughston, Francesco Mina
arXiv · arXiv · 2009
This paper considers the valuation of exotic path-dependent options in Lévy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener--Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a Lévy process. Combined with general results on Fourier methods for option pricing, we provide formulas …
Ernst Eberlein, Kathrin Glau, Antonis Papapantoleon
arXiv · arXiv · 2026
We calibrate credit default swaps and index tranches with elastically stopped Lévy processes: each firm defaults when the running supremum of a latent, spectrally positive distress process crosses an independent exponential barrier. This yields a Cox construction with totally inaccessible default times, while retaining the interpretability and explicit formulas of a structural approach. Adding a single common compoun…
Graeme Baker, Agostino Capponi