INDIFFERENCE PRICING FOR CONTINGENT CLAIMS: LARGE DEVIATIONS EFFECTS
We study utility indifference prices and optimal purchasing quantities for a nontraded contingent claim in an incomplete semimartingale market with vanishing hedging errors. We make connections with the theory of large deviations. We concentrate on sequences of semicomplete markets where in the nth market, the claim Bn admits the decomposition Bn=Dn+Yn . Here, Dn is replicable by trading in the underlying assets Sn , but Yn is independent of Sn . Under broad conditions, we may assume that Yn vanishes in accordance with a large deviations principle (LDP) as n grows. In this setting, for an exponential investor, we identify the limit of the average indifference price pn(qn) , for qn units of Bn , as n→∞ . We show that if |qn|→∞ , the limiting price typically differs from the price obtained by assuming bounded positions supn|qn|<∞ , and the difference is explicitly identifiable using large deviations theory. Furthermore, we show that optimal purchase quantities occur at the large deviations scaling, and hence large positions arise endogenously in this setting.