The Theory of Good-Deal Pricing in Financial Markets

Černý, Aleš; Hodges, Sarah

doi:10.1007/978-3-662-12429-1_9

Cited by 59 publications

(47 citation statements)

References 14 publications

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“…In [18] good deals are defined as investment opportunities characterized by high Sharpe ratios. As discussed in [15], such a definition of good deals is consistent with assuming preference modelling consistent with a quadratic utility functions. Hence, we can consider good-deal pricing based on high Sharpe ratios as being an extension of the Capital Asset Pricing Model.…”

Section: Super-replication and Good Dealsmentioning

confidence: 60%

“…Insofar, good deal pricing using Sharpe ratios is subject to criticisms similar to the ones faced by the CAPM, namely that it only works in a universe of elliptically distributed risks [31]. In a non-elliptical framework, there might be arbitrage opportunities that are not recognized as good deals [15]. To remedy this drawback, it was proposed to use Generalized Sharpe Ratios based on exponential utility functions [42], while this approach was extended to broader classes of utility functions in [14].…”

Section: Super-replication and Good Dealsmentioning

confidence: 99%

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Measurement and Pricing of Risk in Insurance Markets

Tsanakas

Desli

2005

Risk Analysis

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This is the submitted version of the paper.This version of the publication may differ from the final published version. Permanent repository link: AbstractThe theory and practice of risk measurement provides a point of intersection between risk management, economic theories of choice under risk, financial economics and actuarial pricing theory.This paper provides a review of these interrelationships, from the perspective of an insurance company seeking to price the risks that it underwrites. We examine three distinct approaches to insurance risk pricing, all being contingent on the concept of risk measures. Risk measures can be interpreted as representations of risk orderings, as well as absolute (monetary) quantifiers of risk. The first approach can be called an 'axiomatic' one, whereby the price for risks is calculated according to a functional determined by a set of desirable properties. The price of a risk is directly interpreted as a risk measure and may be induced by an economic theory of price under risk. The second approach consists in contextualising the considerations of the risk bearer by embedding them in the market where risks are traded. Prices are calculated by equilibrium arguments, where each economic agent's optimisation problem follows from the minimisation of a risk measure. Finally, in the third approach, weaknesses of the equilibrium approach are addressed by invoking alternative valuation techniques, the leading paradigm among which is arbitrage pricing. Such models move the focus from individual decision takers to abstract market price systems and are thus more parsimonious in the amount of information that they require. In this context, risk * We wish to thank two anonymous referees for their insightful observations, which significantly improved the paper. 1Electronic copy available at: http://ssrn.com/abstract=1006633Electronic copy available at: http://ssrn.com/abstract=1006633measures, instead of characterising individual agents, are used for determining the set of price systems that would be viable in a market.

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Section: Super-replication and Good Dealsmentioning

confidence: 60%

Section: Super-replication and Good Dealsmentioning

confidence: 99%

Measurement and Pricing of Risk in Insurance Markets

Tsanakas

Desli

2005

Risk Analysis

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“…For further discussion we refer the reader to Balbás et al [2]. Now we give our definition of a Good Deal inspired by definitions inČerný and Hodges [7] and Cherny [9]. Definitio 4 A Good Deal is a position X ∈ X such that π(X ) ≤ 0 and ρ(X ) < 0.…”

Section: Definitiomentioning

confidence: 99%

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

Assa

Balbás

2011

Math Finan Econ

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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.

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“…The asterisk denotes 7 See Hansen and Jaganathan (1991), Cerný and Hodges (2001), Jaschke andKücheler (2001), andLongarela (2001) for other models of incomplete markets. See Artzner et al (1999) for risk measures.…”

Section: The Multiperiod Modelmentioning

confidence: 99%

Option-Pricing in Incomplete Markets: The Hedging Portfolio Plus a Risk Premium-Based Recursive Approach

Ibáñez

2005

SSRN Journal

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Consider a non-spanned security C T in an incomplete market. We study the risk/return tradeoffs generated if this security is sold for an arbitrage-free price b C 0 and then hedged. We consider recursive "one-period optimal" self-financing hedging strategies, a simple but tractable criterion.For continuous trading, diffusion processes, the one-period minimum variance portfolio is optimal.Let C 0 (0) be its price. Self-financing implies that the residual risk is equal to the sum of the oneperiod orthogonal hedging errors, P t≤T Y t (0)e r(T −t) . To compensate the residual risk, a risk premium y t ∆t is associated with every Y t . Now let C 0 (y) be the price of the hedging portfolio, and P t≤T (Y t (y) + y t ∆t) e r(T −t) is the total residual risk. Although not the same, the one-period hedging errors Y t (0) and Y t (y) are orthogonal to the trading assets, and are perfectly correlated.This implies that the spanned option payoff does not depend on y. Let bC 0 = C 0 (y). A main result follows. Any arbitrage-free price, b C 0 , is just the price of a hedging portfolio (such as in a complete market), C 0 (0), plus a premium,is the price of the option's payoff which can be spanned, and b C 0 − C 0 (0) is the premium associated with the option's payoff which cannot be spanned (and yields a contingent risk premium of P y t ∆te r(T −t) at maturity). We study other applications of option-pricing theory as well.

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The Theory of Good-Deal Pricing in Financial Markets

Cited by 59 publications

References 14 publications

Measurement and Pricing of Risk in Insurance Markets

Measurement and Pricing of Risk in Insurance Markets

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

Option-Pricing in Incomplete Markets: The Hedging Portfolio Plus a Risk Premium-Based Recursive Approach

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