Binomial valuation of lookback options

Chapter 8 Discrete Barrier and Lookback Options

“…Other lattice methods include adjusting the position of nodes (Ritchken, 1995;Cheuk and Vorst, 1997;Tian, 1999) and refining branching near the barrier Ahn et al, 1999). See also Babbs (1992), Boyle and Lau (1994), Hull and White (1993), Kat (1995).…”

Connecting discrete and continuous path-dependent options

“…Lattice methods for pricing lookback options have been proposed in Babbs [6], Cheuk and Vorst [21], and Hull and White [36], and compared in Kat [38]. The previous work has not explored convergence rates nor examined the modifications necessary to incorporate a predetermined min or max into the algorithm.…”

“…This leads to a very flexible method, but the extra dimension causes a great sacrifice in computational speed. Babbs [6] and Cheuk and Vorst [21] propose a clever transformation that eliminates the added dimension. They do this by constructing a binomial tree for the state variable defined by the ratio of the current minimum (or maximum) price to the current asset price.…”

“…Thus, Theorem 2 is consistent with -and indeed refinesthe approximation arrived at heuristically in (6). 6 Asmussen, Glynn, and Pitman [5] show that √ m(M m −M ) and M are asymptotically independent. It follows through a uniform integrability argument that…”

“…Chance [18], Flesaker [26], Heynen and Kat [34], and Kat and Verdonk [39] discuss the implications of ignoring the discrete-continuous distinction in the context of specific market instruments and give numerical illustrations showing substantial mispricings when, e.g., daily fixings are approximated by continuous monitoring. Computational issues arising in the pricing of discrete path-dependent options are discussed in Andersen and BrothertonRatcliffe [3], Babbs [6], Cheuk and Vorst [21,20], Kat [38], and Levy [43].…”