Two Pricing Methods In The Market Model With Random Interval Payoffs

This paper introduces pricing methods in the market model with random intervalpayoffs. Be different from the traditional market, where all securities’ payoffs arerandom variables, the securities have random interval payoffs. The random intervalcan reflect not only the uncertainty of our market state in the future, but also thefeasible domain of securities when our market will evolve in one state. In the market,there are two kinds of methods for pricing claims, including risk-neutral pricing andindifference pricing.There are two parts in this paper. The first part of the paper is indifference pricingin a single period market with random intervals payoffs. Indifference pricing is such amethod based on utility maximization. Indifference Pricing is an equilibrium price,The maximum expected utility can get when a investor invest the claim, equal to themaximum expected utility can get when a investor don’t invest the claim. Indifferenceprice takes into account the investor’s preference attitude. Paper describes thesituation in general utility function, and analyzes the properties. Such as the unit priceof equity with the bid or ask is how to change the number of units of change, the bidprice is not more than the same kind of interest in ask price, and so on. These are notonly consistent with the traditional market indifference pricing model, but alsoconsistent with the actual situation of the market. Then, paper analyzes theexponential utility function and the binomial model and give numerical example forintroducing calculate indifference price.Next, the paper introduces a multi-period market model with random intervalpayoffs, and how to price contingent claims in this market model. In the traditionalmarket there is self-financing trading strategy which is a basic element in traditional multi-period market model. Because of particularity of random interval, self-financingtrading strategy haven’t been put forward up to now. But the paper apply anotherstrategy called no more financing trading strategy instead, and then define the robustarbitrage opportunity via so-called no more financing trading strategy. Similar to thetraditional random market, our multi-period market is arbitrage-free equivalent toevery single period is arbitrage-free in the multi-period market. Focusing on analysisof the gains process of investors, and the properties of gains process when investorchooses a no more financing trading strategy. In terms of gains process, paperintroduces the definition of a risk-neutral measure, and gives the conclusion thatrisk-neutral measure exists is equivalent to multi-market doesn’t have arbitrageopportunities. At last of this part, paper analyzes contingent claims arbitrage-freepricing, given the non-arbitrage pricing methods.