FinancialDerivative

• FinancialDerivative can compute the values and partial derivatives for many common types of financial derivative contracts.

• FinancialDerivative gives a list of available contracts.

• Contracts are typically specified as a list of the form , where option is the name of the financial instrument, exercise is normally or , and type is either or .

• FinancialDerivative[instrument] lists the names of the contract and ambient parameters.

• FinancialDerivative computes the value of instrument for the specified ambient parameters.

• FinancialDerivative computes multiple properties.

• FinancialDerivative computes all available properties and returns the result as a list of rules.

• Typical contract parameters include:

• The expiration date can be specified as a date, or as the time left to maturity.

• Ambient parameters common to all option types:

• For options on multiple underlying assets, ambient parameters can be given as a list or as a single value common to all underlying assets.

• Volatilities, interest rates, dividends, and the maturity time are assumed to refer to the same time unit, typically years.

• The reference time can be given as a date or as a time difference. If it is not specified, the value is assumed to be today's date.

• Ambient parameter required for basket options, which involve multiple underlying assets:

• The correlation between underlying assets is given as a real symmetric matrix with 1s on the diagonal. All correlation coefficients are in the range to .

• The correlation matrix can also be given as a flat list of the coefficients above the diagonal.

• Ambient currency parameters relevant to Quanto options:

• Properties computed by FinancialDerivative include:

• FinancialDerivative takes the following options:

• Asian Options

• Asian options are a type of option whose value at exercise is computed as the difference between the strike price and the average value of the underlying asset over the lifetime of the contract. FinancialDerivative can valuate the following types of Asian options:

• Contract parameters:

• FinancialDerivative supports Asian call and put options with European exercise style.

• Barrier Options

• Barrier options have a payoff that depends on whether or not the price reaches a predetermined barrier level. The following types of barrier options are supported:

• Barrier up-and-out options become void if the price rises to or exceeds the barrier level. Down-and-out options become void if the price decreases to the barrier. Up-and-in options become valid as the price rises to the barrier level. Down-and-in options become valid when the price falls to or below the barrier level.

• All single-barrier options require the following parameters:

• FinancialDerivative supports call and put barrier options with European and American exercise styles. All rebates are paid at option expiration.

• Binary Options

• Binary or digital options have a payoff at maturity that is either a fixed amount or nothing.

• Binary cash-or-nothing options pay a fixed amount if the underlying price is in the money at maturity. Binary asset-or-nothing options pay the current price of the asset at expiration if the price of the asset is above the strike price.

• Binary options require the following parameters:

• FinancialDerivative supports binary call and put options with European exercise style. The payoff is taken to be 1 for the binary cash option.

• Chooser Options

• A chooser option is a compound contract that requires the buyer to choose between a call and a put option on the same underlying asset at a predetermined expiration time.

• Required contract parameters:

• FinancialDerivative supports chooser options with European exercise style.

• Compound Options

• A compound contract is an option on a European vanilla option.

• Required contract parameters:

• FinancialDerivative supports compound call and put options with European exercise style.

• Double-Barrier Options

• Double-barrier options have a payoff that depends on whether or not the price of the underlying reaches either of the two barrier levels at any time prior to exercise. The following types of double-barrier options are supported:

• A double-barrier knock-out option becomes void as soon as the price of the underlying asset breaks out of the barrier interval. A double-barrier knock-in option becomes valid as soon as the price breaks out of the interval.

• Required contract parameters:

• FinancialDerivative supports double-barrier call and put options with either American or European exercise style.

• Extendible Options

• Extendible options can be exercised at the time of maturity, or they can be extended by a predetermined period. The following types of extendible options are supported:

• A holder-extendible option requires the holder to pay an additional premium to extend the option. A writer-extendible option is extended automatically if the option is out of the money upon initial expiration.

• Required contract parameters:

• FinancialDerivative supports extendible call and put options with European exercise style.

• Lookback Options

• A lookback contract is a path-dependent option whose value at exercise depends on the optimal price of the underlying asset over the lifetime of the contract. The following lookback options are supported:

• In a floating-strike lookback call option, the strike price is taken to be the lowest price attained by the underlying asset over the option's lifetime. For put options, the highest underlying price is used.

• In a fixed-strike lookback call option, the value of the underlying asset at exercise is taken to be the highest price of the underlying asset over the option's lifetime. For put options, the lowest underlying price is used.

• Required contract parameters:

• FinancialDerivative supports lookback call and put options with European exercise style. In addition, it supports American exercise for floating-strike lookback options.

• One-Touch Options

• A one-touch contract is a binary option with an American exercise style.

• One-touch options pay a fixed amount at an arbitrary exercise time if the option is in the money.

• Required contract parameters:

• FinancialDerivative supports one-touch call and put options. The payoff is taken to be 1.

• Option on Future

• An option on a future has a forward contract, rather than a stock security, as its underlying asset.

• Required contract parameters:

• FinancialDerivative supports European call and put options on futures.

• Perpetual Vanilla Options

• A perpetual vanilla contract is an American vanilla option without an expiration date.

• Required contract parameters:

• FinancialDerivative supports American call and put perpetuals.

• Perpetual Lookback Options

• A perpetual lookback contract is a lookback contract without an expiration date.

• In a floating-strike perpetual lookback call option, the strike price adjusts to the lowest price attained by the asset over the contract period so far. For put options, the strike price is taken to be the highest underlying price so far.

• Required contract parameters:

• FinancialDerivative supports floating-strike perpetual lookback call and put options.

• Russian Options

• A Russian option is a type of perpetual lookback call option for which the payoff is the highest value attained by the underlying asset by exercise time.

• Required contract parameters:

• Vanilla Options

• A vanilla option contract is a path-independent option.

• Required contract parameters:

• FinancialDerivative supports vanilla call and put options with either an American or a European exercise style. The name specification can be omitted.

• By default, FinancialDerivative prices American vanilla options by numerically solving the Black-Scholes partial differential equation. A binomial tree solution method can be specified by setting the Method option to .

• Rainbow Options

• A rainbow contract entitles the option holder to the maximum of the payouts generated by the individual components of a basket of assets.

• Option names:

• Required contract parameters:

• FinancialDerivative supports rainbow options with American and European exercise styles. American exercise is supported for a maximum of two non-cash assets in a basket.

• Rainbow Minimum and Maximum Options

• A rainbow minimum contract has a payout that is the value of an option on the worst-performing asset for a call, and on the best-performing asset for a put. A rainbow maximum contract has a payout that is the value of an option on the best-performing asset for a call, and on the worst-performing asset for a put.

• Option names:

• Required contract parameters:

• FinancialDerivative supports rainbow minimum and maximum call and put options with American and European exercise styles. American exercise is supported for a maximum of two assets in a basket.

• Mountain Range Options

• Mountain range options are a class of contracts that entitle the holder to a payout that is based on the performance of a basket of assets, with certain time constraints on asset performance.

• Exercise and option type specifications are not applicable to mountain range options.

• An Altiplano contract is a type of mountain range option that pays out a fixed coupon amount if none of the basket assets have reached their respective barriers, and nothing otherwise.

• Parameters for Altiplano contracts:

• An Annapurna contract pays out a fixed coupon amount if none of the basket assets descend below their respective fractional barrier prices, and nothing otherwise.

• Parameters for Annapurna options:

• An Atlas contract has a payout that is based on the performance of a basket from which the best- and worst-performing assets have been removed.

• Parameters for Atlas contracts:

• An Everest contract has a payout that is based on the performance of the worst asset in a basket of assets.

• Parameters for Everest contracts:

• A Himalaya contract has a payout that is based on the performance of the best asset in a gradually shrinking basket of assets. The time to expiration is divided into subperiods, with the yield for each subperiod determined by the return on the best-performing asset over that period, and with each asset being used to determine a subperiod return exactly once.

• Parameters for Himalaya contracts:

• Spread Options

• A spread contract is a multi-asset option whose value depends on the difference between the values of the underlying assets at the time of exercise.

• Required contract parameters:

• FinancialDerivative supports spread call and put options with American and European exercise styles.

• Quanto Vanilla Options

• A Quanto vanilla contract is an option whose value at exercise depends on the performance of the underlying asset, as well as on the performance of the currency in which the asset is denominated.

• Option names:

• A vanilla fixed-exchange Quanto option is settled at a predetermined exchange rate. A vanilla fixed-strike Quanto option is settled at a fixed strike price in a foreign currency at the prevailing exchange rate.

• Required contract parameters:

• FinancialDerivative supports vanilla Quanto call and put options with American and European exercise styles.