Introduction to Lookback Options
Lookback Option allows an investor to consider the price history when deciding the time to exercise the option. One major benefit of this option is that it helps to lower the uncertainty over the timing of market entry. Also, it lowers the chances of an option going to waste. Of course, with such kind of flexibility available, this option becomes a costly one to execute.
Market also call such an option a hindsight option, and it is a type of exotic option. An exotic option is more complex than a vanilla option, and they usually trade OTC market.
Technical Overview of the Lookback Option:
Lookback call options are financial derivatives that allow their holders to exercise the option by setting the strike price at the minimum of the underlying asset price process (St)t∈[0,T] over the time interval [0,T]. Lookback options can be priced by PDE arguments or by computing the discounted expected values of their claim payoff.
The standard lookback put option gives its holder the right to sell the un- derlying asset at its historically highest price.
Examples :
Scenario 1: Suppose the underlying stock trades at $100 throughout the option period. There is no profit or loss in both fixed and floating strike options in such a scenario.
Scenario 2: Suppose the highest price of the underlying asset during the option period is $200, while the lowest price is $100.
In the case of the fixed option, suppose the strike price is $150. Since the best price was $200 and the strike price was $150, the profit (excluding cost) for the holder would be $50 ($200– $150).
In the case of a floating option, suppose the stock price is $150 at maturity (strike price). Since the lowest price during the option period was $100, the profit (excluding cost) for the holder, in this case, would be $50 ($150 - $100).
Scenario 3: Suppose the stock has the same high and low as above of $200 and $100, respectively, during the option period. However, at maturity, the stock trades at $180.
In the case of a fixed option (with a strike price of $150 set at the time of purchase), the profit (excluding cost) would be the same as above, i.e., $50. This is due to the strike price ($150) being less than the highest price ($200).
Now, in the case of a floating option, suppose the strike price (at the time of maturity) is $180. Since the lowest price is $100, then the profit (excluding cost) for the holder would be $80 ($180 - $100).
Comments