Low-risk management of options to buy or sell assets depends on the ability to effectively control the risk associated with such derivatives through hedging. Under ideal Black-Scholes model assumptions, the price of an option and a corresponding hedging strategy (referred to as delta hedging) can be computed from the solution of PDE's. The ideal hedging strategy requires the continual computation of the spatial derivatives of this solution.

We consider the hedging of a European call option written on the max of two underlying assets. Such a problem is studied on a twodimensional domain as the value of the option depends on the value of both underlying assets. Consequently, the hedging strategy in this case will depend on both components of the gradient. We wish to design an effective mesh that will provide acceptable gradient accuracy over the whole domain considered.

A second element that must be taken into account during mesh design is the time-varying nature of the problem. Since the value of the option is a function of time, the solution profile will become sharper as we near maturity date. Our mesh was hence designed to accommodate for this changing solution profile.

Preliminary error analysis with the designed mesh was carried out on a simple surface with a hyperbolic profile intended to represent the payoff at a given time before expiry. Similar error analysis was carried out using numerical data obtained when solving the PDE equation numerically. Finally, simulations will be carried out to confirm that our mesh provides accurate derivative estimates throughout the life of an option.