Robust pricing and hedging of double no-touch options
- 371 Downloads
Double no-touch options are contracts which pay out a fixed amount provided an underlying asset remains within a given interval. In this work, we establish model-independent bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible.
In addition to establishing rigorous bounds, we consider carefully what is meant by arbitrage in settings where there is no a priori known probability measure. We discuss two natural extensions of the notion of arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are needed to establish equivalence between the lack of arbitrage and the existence of a market model.
KeywordsDouble no-touch option Robust pricing and hedging Skorokhod embedding problem Weak arbitrage Weak free lunch with vanishing risk Model-independent arbitrage
Mathematics Subject Classification (2000)91B28 60G40 60G44
JEL ClassificationC60 G13
Unable to display preview. Download preview PDF.
- 2.Biagini, S., Cont, R.: Model-free representation of pricing rules as conditional expectations. In: Akahori, J., Ogawa, S., Watanabe, S. (eds.) Stochastic Processes and Applications to Mathematical Finance, Proceedings of the 6th Ritsumeikan International Symposium, Kyoto, Japan, 6–10 March 2006, pp. 53–84. World Scientific, Hackensack (2007) Google Scholar
- 13.Cox, A.M.G.: Skorokhod embeddings: non-centred target distributions, diffusions and minimality. http://opus.bath.ac.uk/19625/. Ph.D. thesis, University of Bath (2004)
- 25.Laurent, J.P., Leisen, D.: Building a consistent pricing model from observed option prices. In: Avellaneda, M (ed.) Quantitative Analysis in Financial Markets: Collected Papers of the New York University Mathematical Finance Seminar, vol. 2, pp. 216–238. World Scientific, Singapore (2001) CrossRefGoogle Scholar
- 30.Perkins, E.: The Cereteli–Davis solution to the H 1-embedding problem and an optimal embedding in Brownian motion. In: Seminar on Stochastic Processes, Gainesville, Fla., 1985, pp. 172–223. Birkhäuser Boston, Boston (1986) Google Scholar