α-Quantile Option in a Jump-Diffusion Economy

  • Laura Ballotta
Part of the Applied Optimization book series (APOP, volume 70)


In this note, we extend the analysis of the behaviour of the α-quantile option to the case of a contract’s underlying security driven by a Lévy process. To this aim, a simulation procedure based on the order statistics is implemented. The results produced are also used to study the connections between the occurring of a jump in the market and option prices. In particular, we show that, no matter the risk-neutral valuation framework chosen, the occurring of a jump affects the tails of the distribution of the functional which defines the option payoff. Since options pay a premium for the probability mass existing in the tails of such a distribution, this fact might be seen as a first key to interpret the observed biases.


Lookback option α-quantile option Lévy processes Lévy-Khintchine formula incomplete markets order stastistic. 


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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Laura Ballotta
    • 1
  1. 1.Department of Actuarial Science and Statistics School of MathematicsCity University LondonUK

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