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INDIFFERENCE PRICING FOR CONTINGENT CLAIMS: LARGE DEVIATIONS EFFECTS
Author(s) -
Robertson Scott,
Spiliopoulos Konstantinos
Publication year - 2018
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12137
Subject(s) - semimartingale , economics , limit (mathematics) , large deviations theory , econometrics , mathematical economics , financial market , bounded function , incomplete markets , financial economics , mathematics , microeconomics , statistics , finance , mathematical analysis
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 n th market, the claim B n admits the decompositionB n = D n + Y n . Here, D n is replicable by trading in the underlying assets S n , but Y n is independent of S n . Under broad conditions, we may assume that Y n 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 pricep n ( q n ) , for q n units of B n , as n → ∞ . We show that if| q n | → ∞ , the limiting price typically differs from the price obtained by assuming bounded positionssup n | q n | < ∞ , 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.