Good Deals and compatible modification of risk and pricing rule: a regulatory treatment

Abstract

This work studies Good Deals in a scenario in which a fir uses decision-making tools based on a coherent risk measure, and in which the market prices are determined with a sub-linear pricing rule. The most important observation of this work is that the existence of a Good Deal is equivalent to the incompatibility between the pricing rule and the risk measure. In this paper, we look into this situation from a regulatory point of view to rule out Good Deals with the purpose of stabilizing financia markets. We propose some practical ways of modifying a risk measure so a regulator can set appropriate levels of capital requirements for a financia institution.

A Robust Approach to Hedging and Pricing in Imperfect Markets

“…However, our paper is closely related to another strand of literature, mainly developed in the field of operations research, which is based directly on the concepts of hedging and minimization of risk rather than replication of contingent claims (see Assa and Balbás (2011); Balbás et al (2009Balbás et al ( , 2010 or in a different discipline Smith and Nau (1995)). The main idea is that the financial practitioner tries to minimize the risk of his/her global position, given the budget constraint on a set of manipulatable positions (a set of accessible portfolios, for example).…”

“…The analysis in this setup crucially depends on the sub-additivity property of coherent risk measures and capitalizes on its dual representation. Assa and Balbás (2011) characterize the existence of a solution to the hedging problem and show that a solution exists if and only if there is no costless risk-free position (arbitrage opportunity or Good Deal ). A drawback of their analysis on coherent risk measures is that the hedging is no longer possible for a non-subadditive risk measure such as the popular Value-at-Risk.…”

Hedging and Pricing in Imperfect Markets Under Non-Convexity

“…The robust pricing and hedging strategies of Cox and Ob÷ ój (2011b) and Cox and Ob÷ ój (2011a) serve as an example of this approach. A di¤erent line of research in model-free hedging is based directly on the concepts of hedging and minimization of risk (see Xu (2006), Assa and Balbás (2011), Balbás, Balbás, and Heras (2009), Balbás, Balbás, and Garrido (2010), and Balbás, Balbás, and Mayoral (2009)). In this setting, the investor or portfolio manager minimizes the risk of a global position given the budget constraint on a set of manipulatable positions (a set of accessible portfolios, for instance).…”

“…This non-parametric or robust hedging approach 1 is fairly general and can be used for various purposes such as hedging contingent claims and economic risk variables. While it encompasses the methods developed in Jaschke and Küch-ler (2001), Staum (2004), Xu (2006), Assa and Balbás (2011), Balbás, Balbás, and Heras (2009), Balbás, Balbás, and Garrido (2010), Mayoral (2009), andArai andFukasawa (2014) for sub-additive risk measures and pricing rules, the main novelty of this paper lies in incorporating possibly non-convex risk measures which are extensively used in practice. For example, the celebrated Value at Risk and risk measures related to Choquet expected utility (Bassett, Koenker, and Kordas (2004)) are, in general, non-convex.…”

“…It can be easily veri…ed that x 7 !~ ( x) is the smallest risk measure for which the consistency principle holds. The mapping x 7 !~ ( x) is the market measurement of risk and has been proposed by Assa and Balbás (2011). In this case, Q % = R , which yields % = .…”