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The name extreme spread option might strike you as being a spread option which has some 'extreme' characteristic built in, but in fact, extreme spreads are more a variant of several combined lookback options.
Introduction || Extreme Spread || Reverse Extreme Spread || Binomial Method || Known Names / Variants Options which are based upon two or more assets are commonly generalised as rainbow options. rainbow options which have their value determined by the difference between two or more correlated assets are known as spread options. The name extreme spread option might strike you as being a spread option which has some 'extreme' characteristic built in, but in fact, extreme spreads are more a variant of several combined lookback options. Bermin (1996) introduced these exotics, which he describes as being similar to a fixed strike lookback option, but that the strike is actually floating. That may seem to be a contradiction in its own right, but if you read through the lookbacks section, you'll understand that it is not simply a floating lookback. These options have a payoff at maturity equal to the positive part of the difference between the highest observed price over a period of time near the end of the option period, and the highest price observed during the beginning portion of the option life. One can view the illustration below to see what we mean in the case of extreme spread call options.
In the above diagram, the separation point separates the first and second lookback regions. An extreme spread call option takes the positive difference between points "A" and "B" (i.e. the maximum difference), whereas an extreme spread put would take the spread of the minimum achieved stock prices of each region. These options can be useful for investors who have a well perceived idea of expected market movements within certain future time frames, whilst maximising gains and without being costly. A similar type of this option is a so-called reverse extreme spread option, which is essentially the opposite of a standard extreme spread option, which can be priced using similar formulae to extreme spreads. Pricing: Bermin (1996) produces the formula for all 4 types of extreme spread options. Readers may also find an intepretation in Haug (1998). We make some adjustments to the formulae given by Bermin and Haug in a hope that it will provide clearer representation of the formulation; and although some might prefer the formulae provided by Bermin & Haug, the choice for implementation is up to the reader. Extreme Spread Option
Where,
and
There are three binary variables to consider here; The binary variable M is the observed maximum value of the underlying when S is the asset price at maturity, Additionally, the value of a reverse extreme spread option is given by a similar formula: Reverse Extreme Spread Option
Where the two additional variables G and H are defined as:
The above may strike as being complicated, but it shortens the full valuation formula for each by allocating terms to additional variables. The use of binary variables enables efficient implementation of the algorithm within a programming framework. The graph below shows how changing the minimum (Reverse) / maximum (Extreme) price for the first period affects the price of the reverse extreme spread / extreme spread call option:
Binomial Method: Correlation Options Additional/Useful List of resources Papers: Bermin, H., "Exotic Lookback options: The case of Extreme Spread Options", Working Paper, Department of Economics, Lund University, Sweden (1996) |
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in the equations above takes the value of 1 for a call and -1 for a put. 
takes on 1 in the case of extreme spreads and -1 in the case of reverse extreme spreads. An arbitrary binary variable 
takes the value of 1 for extreme spread options and -1 for a reverse spread option. 
is the final maturity date (or, end of second period), 
is the end of the first period, r is the risk free rate and N(x) is the cumulative normal distribution function of x.
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