It is known that in a jump-diffusion market, it is not possible to hedge perfectly. We are then interested in strategies for hedging an option in some approximate sense. Is it possible to find a portfolio that is a perfect hedge for particular jump-size outcomes of the underlying assets but approximately hedges the option in some mean-averaging sense should the jump-sizes of the underlying assets turn out otherwise? We find that such portfolios usually require an additional number of options of the same type (but with different maturity dates) in order to hedge the option of interest, in a mean-averaging sense.
PhD students: Karl Mina
Contact: Gerald Cheang
GHL Cheang & C Chiarella, 'An Extension of Merton's Jump-Diffusion Model', Proceedings of the Fourth IASTED International Conference on Financial Engineering and Applications, pp. 13-18, Acta Press.