The initial cost of delta hedging, on the other hand, does not change with the frequency of rebalancing; it equals the unique initial lookback option price.
To determine a delta hedge one needs to first choose a risk aversion parameter and then evaluate the risk adjusted lookback option values V(S, t).
The lookback option
was analyzed by Goldman, Sosin, and Gatto (1979).
But then, the premium of the ladder option gradually tends to that of a lookback option.
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):
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.
Exotic Options--Asian Lookback Options
Using Arithmetic Averages.
Therefore, we make use of the probability density function for discrete lookback options in AitSahlia and Lai (1998) to develop our pricing and hedging formulas for the discrete dynamic guaranteed fund.
Lai, 1998, Random Walk Duality and the Valuation of Discrete Lookback Options, Applied Mathematical Finance, 5: 227-240.
After reviewing the technical background, he covers simple exotic options, dual expiry options, two-asset rainbow options, barrier options, lookback options
, Asian options, and exotic multi-options.
Hull and White  developed an efficient procedure for valuing American lookback options
and Asian options.
American and European Options - Barrier Options - Lookback Options
- Zero Cost Collars - Digital Options - Quanto Options - Straddles, Strangles, and Spreads - Asian Options - Outperformance Options