Statistical Methods in Finance 2022

June 28 to July 2, 2022


Optimal Investment And Option Price

By Tatiagoum K. Eric
University of Dschang-Cameroon

In this work, we solve the problem of optimal investment for the hedging of a European option with a portfolio made up of three financial assets: A risky asset of price St , an asset that we qualify as "semi-risky" whose price S ∗ t is a deterministic function of a stochastic interest rate rt and finally, a non-risky asset of price S 0 t . We assume that the payoff Π of the option at maturity date T does not only depend on the strike price ST of the underlying risky asset but also on an unobservable random variable B representing all uncertain events related to the market environment.