Editing Lookback option (section)

==Partial lookback options==
Partial lookback options are a subclass of lookback options with the same payoff structure, but with the goal of reducing its fair price. One way is to scale the fair price linearly with constant <math>\lambda</math>, where <math>0<\lambda<1</math>.<ref>
{{Cite journal
  | last = Conze
  | first = Antoine
  | last2 = Viswanathan
  | date= 1991
  |title= Path dependent options: The case of lookback options
  |journal= The Journal of Finance |volume= 46 | issue = 5
  |pages= 1893–1907 
  |doi= 10.1111/j.1540-6261.1991.tb04648.x
}}</ref> Thus the payoff is:
:<math> \lambda (\max\{S_i\}_1^T - S_T) </math>

Selecting specific dates is a more intricate way of creating partial lookback options and other partial path-dependent options. The principle lies in selecting a subset of monitoring dates, so that the lookback condition is less strong and thus reducing the premium. Examples include the partial lookback option proposed by Heynen and Kat,<ref>
{{Cite journal
  | last = Heynen
  | first = Robert
  | last2 = Harry
  | first2 = Kat
  | date= 1995
  |title= Lookback options with discrete and partial monitoring of the underlying price
  |journal= Applied Mathematical Finance |volume= 2 | issue = 4
  |pages= 273–284 | doi = 10.1080/13504869500000014
  }}</ref> and the amnesiac lookback option proposed by Chang and Li.<ref>
{{Cite journal
  | last = Chang
  | first = Ho-Chun Herbert
  | last2 = Li
  | first2 = Kevin
  | date= 2018
  |title=  The Amnesiac Lookback Option: Selectively Monitored Lookback Options and Cryptocurrencies
  |journal= Frontiers in Applied Mathematics and Statistics |volume= 4 | doi = 10.3389/fams.2018.00010
  | doi-access = free
  }}</ref> Discrete partial path-dependent options are overpriced under continuous assumptions; their pricing is complex and is typically performed using numerical methods.<ref>
{{Cite journal
  | last = Boyarchenko
  | first = Svetlana
  | last2 = Levendorski
  | first2 = Sergei
  | date= 2013
  |title=  Efficient Laplace inversion, Wiener-Hopf factorization and pricing lookbacks
  |journal= International Journal of Theoretical and Applied Finance |volume= 16 | issue = 3
  | pages = 1350011
  | doi = 10.1142/S0219024913500118
  }}</ref><ref>
{{Cite journal
  | last = Feng
  | first = Liming
  | last2 = Linetsky
  | first2 = Vadim
  | date= 2009
  |title=  Computing exponential moments of the discrete maximum of a Lévy process and lookback options
  |journal= Finance and Stochastics |volume= 13 | issue = 3
  | pages = 1350011
  | doi = 10.1142/S0219024913500118
  }}</ref>