# 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.

• Are you sure it is a lookback option? It looks more like an Asian put option because you are using the average of value of S to evaluate the payoff. A lookback put would be using the minimum of S to evaluate the payoff. There are the fixed strike/float strike lookback or average rate/average strike variety for Asian. – stackoverblown May 20 at 19:17
• The place I got it from was an old exam question and it definitely said lookback rate put option. I also thought rate puts were Asian options which is why I was confused here. – Anon May 20 at 20:05