Mark Davis

Imperial College London

Arbitrage bounds for prices of options on realized variance

Abstract: In earlier work with David Hobson [Math Finance 2007] we obtained the arbitrage bounds on a given finite set of quoted call or put options. Here we suppose that a set of such prices is given which is consistent with absence of arbitrage, and we ask what bounds this implies on the price of a weighted variance swap. We exploit the connection between the variance swap and the 'log contract' and similar connections for weighted variance swap. The lower bound becomes a problem in semi-infinite linear programming which we solve in detail. The upper bound is often infinite but, when finite, is easily obtained. We find that market quotes for variance swaps are surprisingly close to the model-free bounds we determine.

Joint work with Jan Oblój and Vimal Raval.