# Pricing Lookback Options

Lookback options let the contract holder trade the underlying asset at the optimum price reached over the life of the contract. They are often purchased by investors who want to avoid the regret of not anticipating the correct market timing.Lookback options are never out of the money and eliminate timing issues with entering and exiting the market.

However, they are more expensive than their vanilla European counterparts and are considered speculative.

With a Lookback call option, the contract isn’t necessarily traded at the market price.  The holder has the benefit of hindsight; they can choose to purchase the asset at its lowest price during the life of the contract.  Conversely, a Fixed Lookback Put allows the holder to sell the asset at the highest price during the life of the contract

The strike price can either be fixed or floating.

• Fixed Lookbacks have the strike determined at purchase
• Floating Lookbacks  have the strike fixed at maturity. Holders of calls have the strike fixed at the lowest price during the life of the contract.  Holders of puts have the strike fixed at the highest price during the life of the contract

## Pricing Lookback Options with Excel

These Excel spreadsheets calculate the price of European style Lookback options. The closed-form analytical equations used to price options with Floating Strikes were derived by Goldman, Sosin & Satto (1979). The corresponding equations used to price Fixed Strikes were taken from Conze & Vizwanathan (1991). The formulas are summarized here.

## 4 thoughts on “Pricing Lookback Options”

1. Lee says:

Thank you for the priceless stuff. Is there a way I can get hold of all the excel files and the VBA code used showing instead of being password protected. Would love to use this in my Phd studies

Thanks

2. gekko says:

Hi, your work is very good.

In Floating Lookback Options, MINIMUM STOCK PRICE is the MIN Stock price for the call and the MAX for the PUT, correct?

Thanks

1. Yes, that’s absolutely correct, and sorry for the ambiguity in the spreadsheet – I’ll correct it!

3. newtonsapple says:

I priced a look back option , witht the following parameters
Time to maturity = 0.083 yrs = 1 month
risk free rate = .25%
volatility 32%
stock price 21.65
Min stock price 19
yield 0

I get a call option price as minus 4.24\$ i.e a negative number , any explanations please