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 semiinfinite 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 modelfree bounds we
determine.
Joint work with Jan Oblój and Vimal Raval.
