Discontinuous Continuity Approximations: Hedging the Next Move
Year: 2026
Type: article
Abstract: Recognizing that in reality price processes display intervals of no price change we construct …nite activity processes capable of synthesizing risk neutral distributions. The proposed construction combines three independent processes, X; N; and G where X and G are Lévy subordinators while N is a standard Poisson process. The …nite activity process is then de…ned as X taken at the time given by N observed at time G; which we call here the XN G process. Ten examples of processes are introduced for di¤erent choices for X and G: Analytical results for the Lévy measure of the XN G processes are presented. In addition we evaluate the quality of the XN G processes as discontinuous continuity approximators. The use of a calibrated …nite activity process gives access to the distribution of the next move. This distribution is employed to build next move hedging strategies that maximize a conservative …nancial valuation of the hedged position. With respect to continuity approximation and hedging sensitivities to the moments of the risk neutral distribution, two of the ten models may be distinguished. These are when G is a …nite actvity process and X has either …nite activity or is a gamma process.
Authors: DILIP B. MADAN, LORENZO TORRICELLI, KING WANG
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7212130624
FWCI:
Cites:
Cited by:
Related to: