Preliminaries

Black Scholes

Just the Black and Scholes formula, together with the delta used for hedging. The input vector is

Inputs

Simulations

This part constructs an array of simulated hedges. The value of the insurance is then computed. Asymptotically, as the rebalancing becomes finer, the value of the hedge should approximate the value of the option it is replicating. The portfolio elements are vectors of the form

The various insurance values are shown below, together with the relevant option price for reference.

It can be seen that the average insurance value is close to the option price. In addition, as the rebalancing interval shrinks, theory says that the deviation of the delta hedging with respect to the option price will go to zero. This can be explored by adjusting the rebalancing interval above.