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Calculate European spread option prices or sensitivities using Bjerksund-Stensland pricing model

Description

example

PriceSens = spreadbybjs(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr) returns the European spread option prices or sensitivities using the Bjerksund-Stensland pricing model.

PriceSens = spreadsensbybjs(___,Name,Value) adds optional name-value pair arguments.

Examples

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Define the spread option dates.

Settle = '01-Jun-2012';
Maturity = '01-Sep-2012';

Define asset 1. Price and volatility of RBOB gasoline

Price1gallon = 2.85;          % \$/gallon
Price1 = Price1gallon * 42;   % \$/barrel
Vol1 = 0.29;

Define asset 2. Price and volatility of WTI crude oil

Price2 = 93.20;         % \$/barrel
Vol2 = 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 the RateSpec.

rates = 0.05;
Compounding = -1;
Basis = 1;
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, ...
'EndDates', Maturity, 'Rates', rates, ...
'Compounding', Compounding, 'Basis', Basis)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: -1
Disc: 0.9876
Rates: 0.0500
EndTimes: 0.2500
StartTimes: 0
EndDates: 735113
StartDates: 735021
ValuationDate: 735021
Basis: 1
EndMonthRule: 1

Define the StockSpec for the two assets.

StockSpec1 = stockspec(Vol1, Price1)
StockSpec1 = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.2900
AssetPrice: 119.7000
DividendType: []
DividendAmounts: 0
ExDividendDates: []

StockSpec2 = stockspec(Vol2, Price2)
StockSpec2 = struct with fields:
FinObj: 'StockSpec'
Sigma: 0.3600
AssetPrice: 93.2000
DividendType: []
DividendAmounts: 0
ExDividendDates: []

Compute the spread option price and sensitivities based on the Kirk model.

OutSpec = {'Price', 'Delta', 'Gamma'};
[Price, Delta, Gamma] = spreadsensbybjs(RateSpec, StockSpec1, StockSpec2, Settle, ...
Maturity, OptSpec, Strike, Corr, 'OutSpec', OutSpec)
Price = 11.2000
Delta = 1×2

0.6737   -0.6082

Gamma = 1×2

0.0190    0.0216

Input Arguments

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Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

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

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

Data Types: struct

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

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

Data Types: struct

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

Data Types: char | cell | double

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

Data Types: char | cell | double

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

Data Types: char | cell

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

If Strike is equal to zero the function computes the price and sensitivities of an exchange option.

Data Types: single | double

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

Data Types: single | double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: PriceSens = spreadsensbykirk(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr,OutSpec,{'All'})

Define outputs, specified as the comma-separated pair consisting of 'OutSpec' and a NOUT- by-1 or 1-by-NOUT cell array of character vectors with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to include each sensitivity:

Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types: char | cell

Output Arguments

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Expected prices or sensitivities values (defined by OutSpec) of the spread option, returned as a NINST-by-1 or NINST-by-2 vector.

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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:

$\mathrm{max}\left(X1-X2-K,0\right)$

where:

K is the strike price.