Approximate Derivative Pricing for Large Class ofHomogeneous Assets

We consider an homogeneous class of assets, whose returns are driven by an unobservablefactor. We derive approximated prediction and pricing formulas for the future factorvalues and their proxies, when the size n of the class is large. Up to order 1=n, these approximationsinvolve solely well-chosen summary statistics of the basic asset returns, butnot lagged factor values.

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Year of publication:	2008-06-01
Authors:	Gagliardini, Patrick ; Gourieroux, Christian
Institutions:	Swiss National Centre of Competence in Research North South <Bern>
Subject:	Preisbildung \| pricing \| Swap \| Kreditrisiko \| Portfoliomanagement \| portfolio management \| Derivat <Wertpapier>

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1 Introduction
2 Homogeneous class of assets
2.1 Definition and assumptions
2.2 Examples
3 Large portfolio approximation
3.1 Approximation theorem
3.2 Approximate pricing formula
3.3 Default and migration correlation
4 Derivatives written on a factor proxy
4.1 Approximate pricing of derivatives written on a default frequency
4.2 Derivatives written on default frequencies vs derivatives writtenon default probabilities
4.3 Approximate pricing of derivatives written on a factor proxy
4.4 Comparison with the literature on large portfolio approximations
5 Numerical illustration to basket default swap
5.1 Parameter values of the one-factor firm value model
5.2 Patterns of factor distributions and derivative prices
5.3 Monte-Carlo
6 Concluding remarks
References
Appendix

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