March 25, 2005: Laurent Cousot, CIMS
Call Options, SemiStatic Arbitrage and Markov Chain Models
A presentation of the paper with abstract:
Under the assumption of the absence of arbitrage, European call prices on a
given asset must satisfy wellknown inequalities, which have been described
in the landmark paper Merton (1973). If we further assume that there is no
interest rate volatility and that the underlying pays continuously
deterministic dividends, cross maturity inequalities must also be satisfied
by the call prices.
In this paper, we show that there exists an arbitrage free model, which is
consistent with the call prices, if these inequalities are satisfied.
Furthermore, we describe an algorithm to obtain a realistic Markov chain
model. The latter is a solution of the problem addressed by local volatility
models since it is calibrated to all available call quotes but does not
require the number of available quotes to be infinite or an interpolation of
the implied volatility surface. Moreover some freedom in the model allows to
have a direct control of the forward implied volatilities. The impact of the
latter on exotics options, e.g. locally capped, globally floored compounding
cliquet options, is investigated numerically.
