spreadsensbybjs

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

Syntax

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

PriceSens = spreadsensbybjs(___,Name,Value)

Description

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

Note

Alternatively, you can use the Spread object to calculate price or sensitivities for spread options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

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

Examples

Compute the Price and Sensitivities of a Spread Option Using the Bjerksund-Stensland Model

Define the spread option dates.

Settle = datetime(2012,6,1);
Maturity = datetime(2012,9,1);

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

RateSpec — Interest-rate term structure

structure

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

StockSpec1 — Stock specification for underlying asset 1

structure

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

StockSpec2 — Stock specification for underlying asset 2

structure

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

Settle — Settlement dates for spread option

datetime array | string array | date character vector

Settlement dates for the spread option, specified a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, spreadsensbybjs also accepts serial date numbers as inputs, but they are not recommended.

Maturity — Maturity date for spread option

datetime array | string array | date character vector

Maturity date for spread option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, spreadsensbybjs also accepts serial date numbers as inputs, but they are not recommended.

OptSpec — Definition of option

character vector with values 'call' or 'put' | cell array of character vectors

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

Data Types: char | cell

Strike — Option strike price values

integer | vector of integers

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: double

Corr — Correlation between underlying asset prices

integer | vector of integers

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

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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

OutSpec — Define outputs

{'Price'} (default) | character vector with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All' | cell array of character vectors with values 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and '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

PriceSens — Expected prices or sensitivities values of spread option

vector

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

More About

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:

$$\max (X1-X2-K,0)$$

where:

K is the strike price.

For more information, see Spread 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.

Version History

Introduced in R2013b

R2022b: Serial date numbers not recommended

Although spreadsensbybjs supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.