Interpreting Lookback Rate Put Options and Their Payoffs

Summary

This question asks what “rate” means in the name of a lookback rate put option. It contrasts an average-rate put, whose payoff depends on the strike and the underlying’s average over the option’s life, with two possible interpretations of a lookback rate put: one involving the maximum price and average price, and another involving the strike and minimum price.

The document does not resolve the terminology or provide an authoritative payoff definition. It is useful as a prompt to distinguish average-rate (Asian) options from lookback options, whose payoff depends on an extreme value reached during the contract. The proposed formulas are guesses from the questioner, so they should not be treated as confirmed contract specifications. The exact payoff depends on how the option is defined by its issuer or governing terms.

Key ideas

• An average-rate put uses the average underlying value over the option’s life in its payoff.
• A lookback option’s payoff can depend on an extreme underlying price observed during the contract.
• The document offers competing payoff interpretations but does not verify either one.
• Contract terminology alone may be insufficient to identify an option’s exact payoff formula.

Tags

# What is a lookback rate put option


# What is a lookback rate put option












I've come across an option called a look-back rate put option. However, the source I got this from did not say what this is. I understand what a look-back put option is, but the rate bit is throwing me off.

The only other seemingly relevant thing that the source says is that an average rate put option has payoff: $max(E-A,0)$ where E is the strike price and A is the average value of S over the options lifetime.

This leads me to believe that a look-back rate put would have a payoff: $$max(J-A,0)$$ where J is the maximum value that the underlying S achieved and A is the average value of S. But it seems that it could also have payoff: $$max(E-L)$$ where E is the exercise price and L is the minimum value that S reached.

Any help clarifying this would be greatly appreciated.

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