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spreadbybjs

Price European spread options using Bjerksund-Stensland pricing model

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Syntax

Price = spreadbybjs(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr)

Description

example

Price= spreadbybjs(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr)returns the price for a European spread option using the Bjerksund-Stensland pricing model.

Examples

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Open Live Script

Define the spread option dates.

Settle ='01-Jan-2012'; Maturity ='01-April-2012';

Define asset 1. Price and volatility of RBOB gasoline

Price1gallon = 2.85;% $/gallonPrice1 = Price1gallon * 42;% $/barrelVol1 = 0.29;

Define asset 2. Price and volatility of WTI crude oil

Price2 = 93.20;% $/barrelVol2 = 0.36;

Define the correlation between the underlying asset prices of asset 1 and asset 2.

Corr = 0.42;

Define the spread option.

OptSpec ='call'; Strike = 20;

Define theRateSpec.

rates = 0.05; Compounding = -1; Basis = 1; RateSpec = intenvset('ValuationDate', Settle,'StartDates', Settle,...'EndDates', Maturity,'Rates', rates,...'Compounding', Compounding,'Basis', Basis)
RateSpec =结构体字段:FinObj: 'RateSpec' Compounding: -1 Disc: 0.9876 Rates: 0.0500 EndTimes: 0.2500 StartTimes: 0 EndDates: 734960 StartDates: 734869 ValuationDate: 734869 Basis: 1 EndMonthRule: 1

Define theStockSpecfor the two assets.

StockSpec1 = stockspec(Vol1, Price1)
StockSpec1 =结构体字段:FinObj: 'StockSpec' Sigma: 0.2900 AssetPrice: 119.7000 DividendType: [] DividendAmounts: 0 ExDividendDates: []
StockSpec2 = stockspec(Vol2, Price2)
StockSpec2 =结构体字段:FinObj: 'StockSpec' Sigma: 0.3600 AssetPrice: 93.2000 DividendType: [] DividendAmounts: 0 ExDividendDates: []

Compute the European spread option price based on the Bjerksund-Stensland model.

Price = spreadbybjs(RateSpec, StockSpec1, StockSpec2, Settle,...Maturity, OptSpec, Strike, Corr)
Price = 11.2000

Input Arguments

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Interest-rate term structure (annualized and continuously compounded), specified by theRateSpecobtained fromintenvset. For information on the interest-rate specification, seeintenvset.

Data Types:struct

Stock specification for underlying asset 1. For information on the stock specification, seestockspec.

stockspeccan handle other types of underlying assets. For example, for physical commodities the price is represented byStockSpec.Asset, the volatility is represented byStockSpec.Sigma, and the convenience yield is represented byStockSpec.DividendAmounts.

Data Types:struct

Stock specification for underlying asset 2. For information on the stock specification, seestockspec.

stockspeccan handle other types of underlying assets. For example, for physical commodities the price is represented byStockSpec.Asset, the volatility is represented byStockSpec.Sigma, and the convenience yield is represented byStockSpec.DividendAmounts.

Data Types:struct

Settlement dates for the spread option, specified as date character vectors or as serial date numbers using aNINST-by-1vector or cell array of character vector dates.

Data Types:double|char|cell

Maturity date for spread option, specified as date character vectors or as serial date numbers using aNINST-by-1vector or cell array of character vector dates.

Data Types:double|char|cell

Definition of option as'call'or'put', specified as aNINST-by-1cell array of character vectors.

Data Types:char|cell

Option strike price values, specified as an integer using aNINST-by-1vector of strike price values.

IfStrikeis equal to zero, the function computes the price of an exchange option.

Data Types:single|double

Correlation between underlying asset prices, specified as an integer using aNINST-by-1vector.

Data Types:single|double

Output Arguments

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Expected prices of the spread option, returned as aNINST-by-1vector.

More About

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Spread Option

Aspread optionis an option written on the difference of two underlying assets.

For example, a European call on the difference of two assetsX1andX2would have the following pay off at maturity:

max ( X 1 − X 2 − K , 0 )

where:

Kis the strike price.

For more information, seeSpread Option.

References

[1] Carmona, R., Durrleman, V. “Pricing and Hedging Spread Options.”SIAM Review.Vol. 45, No. 4, pp. 627–685, Society for Industrial and Applied Mathematics, 2003.

[2] Bjerksund, Petter, Stensland, Gunnar.“Closed form spread option valuation.”Department of Finance, NHH, 2006.

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Introduced in R2013b

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