Abstract
Ross recovery specifies conditions under which it is possible to recover the real-world probability measure as well as the pricing kernel from a family of pricing operators. In this paper, we study Ross recovery theoretically within a semigroup framework using Perron-Frobenius operator theory. Thereby, we derive sufficient conditions guaranteeing existence and uniqueness of a transition independent pricing kernel consistent with the pricing semigroup. Our resultant theory provides a unified perspective on various existing recovery approaches. Building on our theoretical results, we also briefly address the estimation of a pricing semigroup and the corresponding (Markov) transition semigroup from a sample of option prices.
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