This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely...

In general multi-asset models of financial markets, the classic no-arbitrage concepts NFLVR and NUPBR have the serious shortcoming that they depend crucially on the way prices are discounted. To avoid this economically unnatural behaviour, we introduce a new way of defining “absence of...