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Supported Energy Derivatives

Asian Option

An Asian option is a path-dependent option with a payoff linked to the average value of the underlying asset during the life (or some part of the life) of the option. They are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option.

There are four Asian option types, each with its own characteristic payoff formula:

  • Fixed call (average price option):

  • Fixed put (average price option):

  • Floating call (average strike option):

  • Floating put (average strike option):

where:

is the average price of underlying asset.

is the price of the underlying asset.

is the strike price (applicable only to fixed Asian options).

is defined using either a geometric or an arithmetic average.

The following functions support Asian options.

Function

Purpose

asianbyls

Price European or American Asian options using the Longstaff-Schwartz model.

asiansensbyls

Calculate prices and sensitivities of European or American Asian options using the Longstaff-Schwartz model.

asianbykv

Price European geometric Asian options using the Kemna Vorst model.

asiansensbykv

Calculate prices and sensitivities of European geometric Asian options using the Kemna Vorst model.

asianbylevy

Price European arithmetic Asian options using the Levy model.

asiansensbylevy

Calculate prices and sensitivities of European arithmetic Asian options using the Levy model.

Vanilla Option

A vanilla option is a category of options that includes only the most standard components. A vanilla option has an expiration date and straightforward strike price. American-style options and European-style options are both categorized as vanilla options.

The payoff for a vanilla option is as follows:

  • For a call:

  • For a put:

where:

St is the price of the underlying asset at time t.

K is the strike price.

The following functions support specifying or pricing a vanilla option.

Function

Purpose

optstockbyls

Price European, Bermudan, or American vanilla options using the Longstaff-Schwartz model.

optstocksensbyls

Calculate European, Bermudan, or American vanilla option prices and sensitivities using the Longstaff-Schwartz model.

Spread Option

A spread option is an option written on the difference of two underlying assets. For example, a European call on the difference of two assets X1 and X2 would have the following pay off at maturity:

where:

K is the strike price.

The following functions support spread options.

Function

Purpose

spreadbykirk

Price European spread options using the Kirk pricing model.

spreadsensbykirk

Calculate European spread option prices and sensitivities using the Kirk pricing model.

spreadbybjs

Price European spread options using the Bjerksund-Stensland pricing model.

spreadsensbybjs

Calculate European spread option prices and sensitivities using the Bjerksund-Stensland pricing model.

spreadbyfd

Price European or American spread options using the Alternate Direction Implicit (ADI) finite difference method.

spreadsensbyfd

Calculate price and sensitivities of European or American spread options using the Alternate Direction Implicit (ADI) finite difference method.

spreadbyls

Price European or American spread options using Monte Carlo simulations.

spreadsensbyls

Calculate price and sensitivities for European or American spread options using Monte Carlo simulations.

For more information on using spread options, see Pricing European and American Spread Options.

Lookback Option

A lookback option is a path-dependent option based on the maximum or minimum value the underlying asset (e.g. electricity, stock) achieves during the entire life of the option. Basically the holder of the option can ‘look back' over time to determine the payoff. This type of option provides price protection over a selected period, reduces uncertainties with the timing of market entry, moderates the need for the ongoing management, and therefore, is usually more expensive than vanilla options.

Lookback call options give the holder the right to buy the underlying asset at the lowest price. Lookback put options give the right to sell the underlying asset at the highest price.

Financial Instruments Toolbox™ software supports two types of lookback options: fixed and floating. The difference is related to how the strike price is set in the contract.Fixed lookback options have a specified strike price, , and the option pays out the maximum of the difference between the highest (lowest) observed price of the underlying during the life of the option and the strike. Floating lookback options have a strike price determined at maturity, and it is set at the lowest (highest) price of the underlying reached during the life of the option. This means that for a floating strike lookback call (put), the holder has the right to buy (sell) the underlying asset at its lowest (highest) price observed during the life of the option. Consequently, there are a total of four lookback option types, each with its own characteristic payoff formula:

  • Fixed call:

  • Fixed put:

  • Floating call:

  • Floating put:

where:

is the maximum price of underlying asset.

is the minimum price of underlying asset.

is the price of the underlying asset at maturity.

is the strike price.

The following functions support lookback options.

Function

Purpose

lookbackbycvgsg

Calculate prices of European lookback fixed and floating strike options using the Conze-Viswanathan and Goldman-Sosin-Gatto models.

lookbacksensbycvgsg

Calculate prices and sensitivities of European fixed and floating strike lookback options using the Conze-Viswanathan and Goldman-Sosin-Gatto models.

lookbackbyls

Calculate prices of lookback fixed and floating strike options using the Longstaff-Schwartz model.

lookbacksensbyls

Calculate prices and sensitivities of lookback fixed and floating strike options using the Longstaff-Schwartz model.

Lookback options as well as Asian options are instruments used in the electricity market to manage purchase timing risk. Electricity purchasers cover part of their expected electricity consumption on the forward market to avoid the volatility and limited liquidity of the spot market. Using Asian options as a hedging tool is a passive approach to solving the purchase timing problem. An Asian option instrument diminishes the wrong timing risk but it also reduces any potential benefit to the buyer from falling prices. On the other hand, lookback options allow the purchasers to buy electricity at the lowest price, but as mentioned before, this instrument is more expensive than Asian and vanilla options.

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