Pricing multi-asset barrier options

• Main Author: Rosalino Junior, Estevão
• Publication Date: 2018
• Format: Doctoral thesis
• Language: eng
• Source: Biblioteca Digital de Teses e Dissertações do LNCC
• Download full: https://tede.lncc.br/handle/tede/306
• topic: Preços; Especulação (Finanças); Multi-asset barrier options; CNPQ::CIENCIAS SOCIAIS APLICADAS::ECONOMIA

This thesis contributes, theoretically, in the multi-asset scenario with closed-form ex- pressions of no-arbitrage prices, as well as estimates, for an assortment of multi-asset up-and-out call barrier options. A novelty for the estimates is that we combine ideas of convex analysis with tools of stochastic theory. We also provide an expression for deriving numerically a certain joint density function and, from this, some option prices. The barrier options presented herein are of two kinds. The first one is when each asset is tested, individually, against its corresponding barrier. The second one considers hyperplane barriers placed on the collection (or vector) of stock prices. Concerning the risky assets, the uncorrelated as well as the correlated case is addressed. The models under concern have deterministic time dependent volatility. It is worth noticing that deriving prices in the multi-asset case poses significant difficulties that do not appear in the single-asset case.