Asian option
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An Asian option (or average value option) is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different to the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at maturity.
One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity[1].
[edit] Payout of Asian call options with arithmetic average
We describe the payout of some Asian call options.
The continuous case gives the payout
where T is the time to maturity, S is the price and K is the strike price.
For the case of discrete monitoring (with monitoring at the times 
) we have the payout
There exist Asian options using geometric average, as well as arithmetic average.
[edit] Pricing of Asian options
A discussion of the problem of pricing Asian options with Monte Carlo methods is given in a paper by Kemna and Vorst. [2]
Rogers and Shi solve the pricing problem with a PDE approach [3].
Variance Gamma model can be efficiently implemented when pricing Asian style options. Then using the Bondesson series representation for generating the variance gamma process shows to have some advantages when pricing this type of option. [4]
[edit] References
- ^ Kemna et al. 1990, p 1077
- ^ Kemna, A.G.Z.; Vorst, A.C.F.; Rotterdam, E.U.; Instituut, Econometrisch (1990), A Pricing Method for Options Based on Average Asset Values, http://ideas.repec.org/a/eee/jbfina/v14y1990i1p113-129.html
- ^ Rogers, L.C.G.; Shi, Z. (1995), "The value of an Asian option", Journal of Applied Probability 32: 1077–1088, http://www.institut.math.jussieu.fr/~boka/enseignement/isifar/refs/Ref_Asiatiques_Rogers_Shi_95.pdf
- ^ Mattias Sander. Bondesson's Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008
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