α-Quantile Option in a Jump-Diffusion Economy
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.
KeywordsLookback option α-quantile option Lévy processes Lévy-Khintchine formula incomplete markets order stastistic.
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