# lookback call option

## Lookback Call Option

A call option giving the holder the right (but not the obligation) to buy the underlying asset on or by the expiration date at its lowest price that occurred between the start of the option and the time it is exercised. Because there is no set strike price and the lookback gives the option holder the highest possible flexibility, it carries a high premium (or sale price). See also: Lookback Put Option.

## lookback call option

A specialized option that gives its owner the right to purchase the underlying asset at the lowest price at which it traded between the effective date and the expiration date of the option. The added advantage of being able to look back makes this option command a relatively high premium.
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Consider a European lookback call option with fixed strike, with payoff ([bar.S] - K)+, where [bar.S] is the maximum of the stock price between time 0 and time T.
Given a finite time horizon T > 0, let C = C(t, S, m) be the value of the American fractional lookback call option at time t [member of] [0, T].
At the early exercise boundary [[bar.S](i, m)].sub.t[member of][0,T]], the American fractional lookback call option would be optimally exercised.
In the same way as in the call case, by (63), (70), (71), (72), (76), (77), and (78), we can formulate the put case: Let P = P(t, S, m) be the value of the American fractional lookback call option at time t [member of] [0, T].
Comparing with Theorem 17 and Corollary 20, the optimal exercise boundary and Volterra integral equation of American fractional lookback call option are obvious as follows.
Let [V.sup.*] (t, S, m) be American fractional lookback call option; then
Similarly, the critical exercise price for the American fractional floating strike lookback call option should be denoted as
Note that the first order approximation for the floating lookback call option [LC.sub.fl] is given by
(10.) A lookback straddle consists of a lookback call option and a lookback put option.

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