We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case. © 2011 World Scientific Publishing Company.

Mercuri, L. (2011). Pricing asian options in affine garch models. INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, 14(2), 313-333 [10.1142/S0219024911006371].

Pricing asian options in affine garch models

MERCURI, LORENZO
2011

Abstract

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case. © 2011 World Scientific Publishing Company.
Articolo in rivista - Articolo scientifico
Asian options; affine Garch models; Fourier transform; semi-analytical valuation; Edgeworth series
English
313
333
Mercuri, L. (2011). Pricing asian options in affine garch models. INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, 14(2), 313-333 [10.1142/S0219024911006371].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/25587
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
Social impact