Discrete approximation of risk-based prices under volatility uncertainty

Jonas Blessing, Michael Kupper and Alessandro Sgarabottolo
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Jonas Blessing: Center for Mathematical Economics, Bielefeld University
Michael Kupper: Center for Mathematical Economics, Bielefeld University
Alessandro Sgarabottolo: Center for Mathematical Economics, Bielefeld University

No 742, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The asymptotic riskbased prices form a strongly continuous convex monotone semigroup which is uniquely determined by its infinitesimal generator and therefore only depends on the covariance of the random factors but not on the particular choice of the model. We further compare the risk-based prices with the worst-case prices given by the G-expectation and investigate their asymptotic behaviour as the risk aversion of the agent tends to infinity. The theoretical results are illustrated with several examples and numerical simulations showing, in particular, that the risk-based prices lead to a significant reduction of the bid-ask spread compared to the worst-case prices.

Keywords: risk-based pricing; indifference pricing; volatility uncertainty; nonlinear semigroup; Chernoff approximation (search for similar items in EconPapers)
Pages: 36
Date: 2025-08-18
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