Implied trees in illiquid markets: A Choquet pricing approach

Implied trees are necessary to implement the risk neutral valuation approach, and standard methodologies for their derivation are based on the validity of the put call parity. However, in illiquid markets the put call parity fails to hold, and the uniqueness of the artificial probabilities leaves room for an interval. The contribution of this article is twofold. First we propose a methodology for the derivation of implied trees in illiquid markets. Such a methodology, by contrast with standard ones, takes into account the information stemming both from call and put prices. Second, we set up a framework for pricing derivatives written on an underlying asset traded on an illiquid market. To this end we have extended the Choquet integral definition to account for interval payoffs of the underlying asset. The price interval we obtain may be interpreted as a bid-ask price quoted by the intermediary issuing the derivative security.