Extending Pricing Rules with General Risk Functions Articles uri icon

publication date

  • February 2010

start page

  • 23

end page

  • 33

issue

  • 1

volume

  • 201

international standard serial number (ISSN)

  • 0377-2217

electronic international standard serial number (EISSN)

  • 1872-6860

abstract

  • The paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging strategy is measured by a general risk function. Convex Optimization Theory is used in order to
    extend pricing rules for a wide family of risk functions, including
    Deviation Measures, Expectation Bounded Risk Measures and Coherent
    Measures of Risk. Necessary and sufficient optimality conditions are
    provided in a very general setting. For imperfect markets the extended
    pricing rules reduce the bid-ask spread. The findings are particularized
    so as to study with more detail some concrete examples, including the
    Conditional Value at Risk and some properties of the Standard Deviation.
    Applications dealing with the valuation of volatility linked
    derivatives are discussed.