Abstract:
The paper presents a financial market model that generates stochastic volatility using a
minimal set of factors. These factors, formed by transformations of square root processes,
model the dynamics of different denominations of a benchmark portfolio. Benchmarked
prices are assumed to be local martingales. Numerical results for the pricing and hedging
of basic derivatives on indices are described for the minimal market model. This
includes cases where the standard risk neutral pricing methodology fails because of the
presence of a strict local martingale measure. However, payoffs can be perfectly hedged
using self-financing strategies and a form of arbitrage exists. This is illustrated by hedge
simulations. The different term structure of implied volatilities is documented for calls
and puts on an index.
