Preliminaries

As usually, one has to initialize, load a few useful packages and set the global variables. In this example one wishes to hedge gold using silver futures. The assumption is made that the futures price is given by the relationship . The prices of gold and silver are simulated, and a correlation between them is assumed.

Simulations

Basis points and basis risk

The graphs below show the prices for gold and its futures, and silver and its futures. One can easily observe the futures-spot convergence, which is present by construction.

The basis is defined, and is susequently graphed. It is easy to verify that as the maturity is approached, the gold and silver basis converge to zero. This happens of course due to the futures-spot convergence.  On the other hand, the cross basis does not converge to zero: as expected, there is some basis risk, due to the fact that we use silver futures to hedge the price of gold.

Marking to market

We now turn the mark-to-market procedure. Suppose that gold futures are purchased. The initial margin is set at 10% of the overall position, whereas the maintenance margin is set at 7% of the overall position. One can see how the margin account detiorates as the futures price falls, with a margin call occuring in period 14. For simplicity the added assumption has been made that the margin account does not offer interest, although the code can be easily altered to incorporate that feature. The periods 15-89 are deleted from this output.

The graph below visualises the evolution of the margin account across time. The margin, initial and maintenance are given by the solid lines. The periods when money has been required to be transferred into the account are denoted by grey.

The period-by-period profits and losses of the futures position are given in the bar chart below. The margin calls, together with the initial margin are given in black.