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Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints

: Desmettre, S.; Laudagé, C.; Sass, J.

Fulltext ()

Risks 8 (2020), No.4, Art. 114, 22 pp.
ISSN: 2227-9091
Journal Article, Electronic Publication
Fraunhofer ITWM ()

In this paper, we deal with the pricing of European options in an incomplete market. We use the common risk measures Value-at-Risk and Expected Shortfall to define good-deals on a financial market with log-normally distributed rate of returns. We show that the pricing bounds obtained from the Value-at-Risk admit a non-smooth behavior under parameter changes. Additionally, we find situations in which the seller’s bound for a call option is smaller than the buyer’s bound. We identify the missing convexity of the Value-at-Risk as main reason for this behavior. Due to the strong connection between good-deal bounds and the theory of risk measures, we further obtain new insights in the finiteness and the continuity of risk measures based on multiple eligible assets in our setting.