Positive Stochastic Collocation for the Collocated Local Volatility Model
Pricing of Securities
2021-09-07 v1 Computational Finance
Mathematical Finance
Risk Management
Abstract
This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary. It shows that the polynomial collocation towards a lognormal distribution does not work well. Then, the potentials issues of the related collocated local volatility model (CLV) are explored. Finally, a simple analytical expression for the Dupire local volatility derived from the option prices modelled by stochastic collocation is given.
Cite
@article{arxiv.2109.02405,
title = {Positive Stochastic Collocation for the Collocated Local Volatility Model},
author = {Fabien Le Floc'h and Cornelis W. Oosterlee},
journal= {arXiv preprint arXiv:2109.02405},
year = {2021}
}