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2018

Derivatives pricing using signature payoffs

Arribas, Imanol Perez

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We introduce signature payoffs, a family of path-dependent derivatives that are given in terms of the signature of the price path of the underlying asset.

We show that these derivatives are dense in the space of continuous payoffs, a result that is exploited to quickly price arbitrary continuous payoffs.
This approach to pricing derivatives is then tested with European options, American options, Asian options, lookback options and variance swaps.
As we show, signature payoffs can be used to price these derivatives with very high accuracy.

Derivatives pricing using signature payoffs · Around

Built on

Stone, M. H. (1948). The generalized Weierstrass approximation theorem
Original
1948
Earlier work this paper cites.
Delbaen, F., & Schachermayer, W. (1994). A general version of the fundamental theorem of asset pricing
1994
Earlier work this paper cites.
Fawcett, T. (2002)
2002
Earlier work this paper cites.
Lyons, T. J., Caruana, M., & Lévy, T. (2007)
2007
Earlier work this paper cites.

Similar

Friz, P. K., & Victoir, N. B. (2010)
2010
Cited alongside, same era.
Hambly, B., & Lyons, T. (2010). Uniqueness for the signature of a path of bounded variation and the reduced path group
2010
Cited alongside, same era.
Ni, H. (2012)
2012
Cited alongside, same era.

Then

Levin, D., Lyons, T., & Ni, H. (2013). Learning from the past, predicting the statistics for the future, learning an evolving system
Original
2013
Later among the works it cites.
Boedihardjo, H., Geng, X., Lyons, T., & Yang, D. (2016). The signature of a rough path: uniqueness
2016
Later among the works it cites.
Chevyrev, I., & Lyons, T. (2016). Characteristic functions of measures on geometric rough paths
2016
Later among the works it cites.

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