Skewness and kurtosis thus have a significant effect on lookback option
prices; the effect will of course vary depending on the parameters.
Further, to capture jumps or discontinuous, fluctuations problem or take into account long memory property, we present here a new method to solve option pricing problem for American lookback option
in a mixed jump-diffusion fractional Brownian motion environment.
As a kind of exotic options, the holder of lookback option
could look back on the evolution process of underlying assets during the life of option at maturity.
If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (nonstandard lookback option
) and [LC.sub.fl](L s, m, T) denotes the price of the floating strike lookback call on [S.sub.t] = s with realized minimum m and time to maturity T, then one can obtain the following result.
The Adjusted [R.sup.2] and F values in Table VII suggest that the average-strike put option model performs relatively better (worse) on the noninformation-intensive (information-intensive) subsample and that the lookback option
model does the reverse.
The type of contract that provides this feature to its fullest extent is the lookback option
, whose payoff at expiry T writes (for a call with fixed strike):
The lookback option
was analyzed by Goldman, Sosin, and Gatto (1979).
For example, Longstaff  approximates the marketability values of a security as a continuous-time lookback option
. Barrier options are inherent in the reduced-form approach to credit risk, where the default time of a company is modeled as the first hitting time, or barrier breaching time, of the asset process of the company; see Merton , Black and Cox , Leland and Toft , and Chen and Kou .
The option embedded in a variable annuity with a ratchet GMDB is a path dependent lookback option
. The payoff of GMDB with a ratchet feature is
Many exotic options, including binary options, lookback options
, and "as-you-like-it" options center around the interests of speculators rather than hedgers, although hedging is, in actuality, the most elementary function of options.
Subsequently, he extended Babbs method on the basis of Black-Scholes model to construct a trinomial tree method for evaluating the lookback options
under the CEV model, as was translated into Chinese by He (2001).
European floating strike lookback options
are a different interesting kind of GULC.