spreadbykirk

Price European spread options using Kirk pricing model

Syntax

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

Description

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

Examples

Compute the Price of a Spread Option Using the Kirk Model

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;          % $/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: 734960
       StartDates: 734869
    ValuationDate: 734869
            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 European spread option price based on the Kirk model.

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

Price = 11.1904

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

serial date number | vector of serial date numbers | date character vector | cell array of character vectors

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: double | char | cell

Maturity — Maturity date for spread option

serial date number | vector of serial date numbers | date character vector | cell array of date character vectors

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: double | char | cell

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: cell | char

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 0, the function computes the price of an exchange option.

Data Types: single | 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: single | double

Output Arguments

Price — Expected prices of spread option

vector

Expected prices of the spread option, returned as a NINST-by-1 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.