optstockbyblk

Price options on futures and forwards using Black option pricing model

Syntax

Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity,
OptSpec, Strike)
Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity,
OptSpec, Strike, ForwardMaturity)

Arguments

RateSpec

The annualized continuously compounded rate term structure. For information on the interest rate specification, see intenvset.

StockSpec

Stock specification. See stockspec.

Settle

NINST-by-1 vector of settlement or trade dates.

Maturity

NINST-by-1 vector of maturity dates for the option.

OptSpec

NINST-by-1 cell array of strings 'call' or 'put'.

Strike

NINST-by-1 vector of strike price values.

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

ForwardMaturity

(Optional) NINST-by-1 maturity date or delivery date of the forward contract. The default is equal to the Maturity of the option.

Description

Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity,
OptSpec, Strike)
computes option prices on futures using the Black option pricing model.

Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity,
OptSpec, Strike, ForwardMaturity)
computes option prices on forwards using the Black option pricing model.

Price is a NINST-by-1 vector of expected option prices.

    Note:   optstockbyblk calculates option prices on futures and forwards. If ForwardMaturity is not passed, the function calculates prices of future options. If ForwardMaturity is passed, the function computes prices of forward options. This function handles several types of underlying assets, for example, stocks and commodities. For more information on the underlying asset specification, see stockspec.

Examples

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Compute Option Prices on Futures Using the Black Option Pricing Model

This example shows how to compute option prices on futures using the Black option pricing model. Consider two European call options on a futures contract with exercise prices of $20 and $25 that expire on September 1, 2008. Assume that on May 1, 2008 the contract is trading at $20, and has a volatility of 35% per annum. The risk-free rate is 4% per annum. Using this data, calculate the price of the call futures options using the Black model.

Strike = [20; 25];
AssetPrice = 20;
Sigma = .35;
Rates = 0.04;
Settle = 'May-01-08';
Maturity = 'Sep-01-08';

% define the RateSpec and StockSpec
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
 'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1);

StockSpec = stockspec(Sigma, AssetPrice);

% define the call options
OptSpec = {'call'};

Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity,...
OptSpec, Strike)
Price =

    1.5903
    0.3037

Compute Option Prices on a Forward

This example shows how to compute option prices on forwards using the Black pricing model. Consider two European options, a call and put on the Brent Blend forward contract that expires on January 1, 2015. The options expire on October 1, 2014 with an exercise price of $200 and $98 respectively. Assume that on January 1, 2014 the forward price is at $107, the annualized continuously compounded risk-free rate is 3% per annum and volatility is 28% per annum. Using this data, compute the price of the options.

Define the RateSpec.

ValuationDate = 'Jan-1-2014';
EndDates = 'Jan-1-2015';
Rates = 0.03;
Compounding = -1;
Basis = 1;
RateSpec  = intenvset('ValuationDate', ValuationDate, ...
'StartDates', ValuationDate, 'EndDates', EndDates, 'Rates', Rates,....
'Compounding', Compounding, 'Basis', Basis')
RateSpec = 

           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9704
            Rates: 0.0300
         EndTimes: 1
       StartTimes: 0
         EndDates: 735965
       StartDates: 735600
    ValuationDate: 735600
            Basis: 1
     EndMonthRule: 1

Define the StockSpec.

AssetPrice = 107;
Sigma = 0.28;
StockSpec  = stockspec(Sigma, AssetPrice);

Define the options.

Settle = 'Jan-1-2014';
Maturity = 'Oct-1-2014';  %Options maturity
Strike = [200;90];
OptSpec = {'call'; 'put'};

Price the forward call and put options.

ForwardMaturity = 'Jan-1-2015';  % Forward contract maturity
Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike,...
'ForwardMaturity', ForwardMaturity)
Price =

    0.0535
    3.2111

Compute the Option Price on a Future

Consider a call European option on the Crude Oil Brent futures. The option expires on December 1, 2014 with an exercise price of $120. Assume that on April 1, 2014 futures price is at $105, the annualized continuously compounded risk-free rate is 3.5% per annum and volatility is 22% per annum. Using this data, compute the price of the option.

Define the RateSpec.

ValuationDate = 'January-1-2014';
EndDates = 'January-1-2015';
Rates = 0.035;
Compounding = -1;
Basis = 1;
RateSpec  = intenvset('ValuationDate', ValuationDate, 'StartDates', ValuationDate,...
'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis')
RateSpec = 

           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9656
            Rates: 0.0350
         EndTimes: 1
       StartTimes: 0
         EndDates: 735965
       StartDates: 735600
    ValuationDate: 735600
            Basis: 1
     EndMonthRule: 1

Define the StockSpec.

AssetPrice = 105;
Sigma = 0.22;
StockSpec  = stockspec(Sigma, AssetPrice)
StockSpec = 

             FinObj: 'StockSpec'
              Sigma: 0.2200
         AssetPrice: 105
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Define the option.

Settle = 'April-1-2014';
Maturity = 'Dec-1-2014';
Strike = 120;
OptSpec = {'call'};

Price the futures call option.

Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)
Price =

    2.5847

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