We investigate the pricing of cliquet options in a jump-diffusion model. The
considered option is of monthly sum cap style while the underlying stock price
model is driven by a drifted L\'{e}vy process entailing a Brownian diffusion
component as well as compound Poisson jumps. We also derive representations for
the density and distribution function of the emerging L\'{e}vy process. In this
setting, we infer semi-analytic expressions for the cliquet option price by two
different approaches. The first one involves the probability distribution
function of the driving L\'{e}vy process whereas the second draws upon Fourier
transform techniques. With view on sensitivity analysis and hedging purposes,
we eventually deduce representations for several Greeks while putting emphasis
on the Vega.Comment: Published at https://doi.org/10.15559/18-VMSTA107 in the Modern
Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA)
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