Fast binomial procedures for pricing Parisian/ParAsian options

Marcellino Gaudenzi (1) , Antonino Zanette (1)

1 MATHRISK - Mathematical Risk handling

The discrete procedures for pricing Parisian/ParAsian options depend, in general, on three dimensions: time, space, time spent over the barrier. Here we present some combinatorial and lattice procedures which reduce the computational complexity to second order. In the European case the reduction was already given by Lyuu-Wu [11] and Li-Zhao [10], in this paper we present a more efficient procedure in the Parisian case and a different approach (again of order 2) in the ParAsian case. In the American case we present new procedures which decrease the complexity of the pricing problem for the Parisian/ParAsian knock-in options. The reduction of complexity for Parisian/ParAsian knockout options is still an open problem.

Mots clés: tree methods; binomial methods; ParAsian options; combinatorial formula; Parisian options

Domaines: Probabilités [math.PR]

Marcellino Gaudenzi, Antonino Zanette. Fast binomial procedures for pricing Parisian/ParAsian options. Computational Management Science, 2017, 14 (3), pp.313-331. ⟨10.1007/s10287-017-0278-5⟩. ⟨hal-01632859⟩