Price options on futures and forwards using Black option pricing model
collapse all in page
Syntax
Price = optstockbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)
Price = optstockbyblk(___,Name,Value)
Description
Price = optstockbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) computes option prices on futures or forward using the Black option pricing model.
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.
Price = optstockbyblk(___,Name,Value) adds an optional name-value pair argument for ForwardMaturity to compute option prices on forwards using the Black option pricing model.
Examples
collapse all
Compute Option Prices on Futures Using the Black Option Pricing Model
Open Live Script
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 = datetime(2008,5,1);Maturity = datetime(2008,9,1);% define the RateSpec and StockSpecRateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1);StockSpec = stockspec(Sigma, AssetPrice);% define the call optionsOptSpec = {'call'};Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity,...OptSpec, Strike)
Price = 2×1 1.5903 0.3037Compute Option Prices on a Forward
Open Live Script
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 $90 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 = datetime(2014,1,1);EndDates = datetime(2015,1,1);Rates = 0.03;Compounding = -1;Basis = 1;RateSpec = intenvset('ValuationDate', ValuationDate, ...'StartDates', ValuationDate, 'EndDates', EndDates, 'Rates', Rates,....'Compounding', Compounding, 'Basis', Basis')
RateSpec = struct with fields: FinObj: 'RateSpec' Compounding: -1 Disc: 0.9704 Rates: 0.0300 EndTimes: 1 StartTimes: 0 EndDates: 735965 StartDates: 735600 ValuationDate: 735600 Basis: 1 EndMonthRule: 1Define the StockSpec.
AssetPrice = 107;Sigma = 0.28;StockSpec = stockspec(Sigma, AssetPrice);
Define the options.
Settle = datetime(2014,1,1);Maturity = datetime(2014,10,1); %Options maturityStrike = [200;90];OptSpec = {'call'; 'put'};
Price the forward call and put options.
ForwardMaturity = 'Jan-1-2015'; % Forward contract maturityPrice = optstockbyblk(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike,...'ForwardMaturity', ForwardMaturity)
Price = 2×1 0.0535 3.2111Compute the Option Price on a Future
Open Live Script
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 = datetime(2014,1,1);EndDates = datetime(2015,1,1);Rates = 0.035;Compounding = -1;Basis = 1;RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', ValuationDate,...'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis')
RateSpec = struct with fields: FinObj: 'RateSpec' Compounding: -1 Disc: 0.9656 Rates: 0.0350 EndTimes: 1 StartTimes: 0 EndDates: 735965 StartDates: 735600 ValuationDate: 735600 Basis: 1 EndMonthRule: 1Define the StockSpec.
AssetPrice = 105;Sigma = 0.22;StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields: FinObj: 'StockSpec' Sigma: 0.2200 AssetPrice: 105 DividendType: [] DividendAmounts: 0 ExDividendDates: []Define the option.
Settle = datetime(2014,4,1);Maturity = datetime(2014,12,1); Strike = 120;OptSpec = {'call'};Price the futures call option.
Price = optstockbyblk(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)
Price = 2.5847
Input Arguments
collapse all
StockSpec — Stock specification for underlying asset
structure
Stock specification for the underlying asset. For information on the stock specification, see stockspec.
stockspec handles several types of underlying assets. For example, for physical commodities the price is StockSpec.Asset, the volatility is StockSpec.Sigma, and the convenience yield is StockSpec.DividendAmounts.
Data Types: struct
Settle — Settlement or trade date
datetime array | string array | date character vector
Settlement or trade date, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.
To support existing code, optstockbyblk also accepts serial date numbers as inputs, but they are not recommended.
Maturity — Maturity date for option
datetime array | string array | date character vector
Maturity date for option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.
To support existing code, optstockbyblk also accepts serial date numbers as inputs, but they are not recommended.
OptSpec — Definition of option
cell array of character vectors with values 'call' or 'put'
Definition of the option as 'call' or 'put', specified as a NINST-by-1 cell array of character vectors with values 'call' or 'put'.
Data Types: cell
Strike — Option strike price value
nonnegative vector
Option strike price value, specified as a nonnegative 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: Price = optstockbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'ForwardMaturity',ForwardMaturity)
ForwardMaturity — Maturity date or delivery date of forward contract
Maturity of option (default) | date character vector
Maturity date or delivery date of forward contract, specified as the comma-separated pair consisting of 'ForwardMaturity' and a NINST-by-1 vector using date character vectors.
To support existing code, optstockbyblk also accepts serial date numbers as inputs, but they are not recommended.
Output Arguments
collapse all
Price — Expected option prices
vector
Expected option prices, returned as a NINST-by-1 vector.
More About
collapse all
Futures Option
A futures option is a standardized contract between two parties to buy or sell a specified asset of standardized quantity and quality for a price agreed upon today (the futures price) with delivery and payment occurring at a specified future date, the delivery date.
The futures contracts are negotiated at a futures exchange, which acts as an intermediary between the two parties. The party agreeing to buy the underlying asset in the future, the "buyer" of the contract, is said to be "long," and the party agreeing to sell the asset in the future, the "seller" of the contract, is said to be "short."
A futures contract is the delivery of item J at time T and:
There exists in the market a quoted price , which is known as the futures price at time t for delivery of J at time T.
The price of entering a futures contract is equal to zero.
During any time interval [t,s], the holder receives the amount (this reflects instantaneous marking to market).
At time T, the holder pays and is entitled to receive J. Note that should be the spot price of J at time T.
For more information, see Futures Option.
Forwards Option
A forwards option is a non-standardized contract between two parties to buy or to sell an asset at a specified future time at a price agreed upon today.
The buyer of a forwards option contract has the right to hold a particular forward position at a specific price any time before the option expires. The forwards option seller holds the opposite forward position when the buyer exercises the option. A call option is the right to enter into a long forward position and a put option is the right to enter into a short forward position. A closely related contract is a futures contract. A forward is like a futures in that it specifies the exchange of goods for a specified price at a specified future date.
The payoff for a forwards option, where the value of a forward position at maturity depends on the relationship between the delivery price (K) and the underlying price (ST) at that time, is:
For a long position:
For a short position:
For more information, see Forwards Option.
Version History
Introduced in R2008b
expand all
R2022b: Serial date numbers not recommended
Although optstockbyblk 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.
Open Example
You have a modified version of this example. Do you want to open this example with your edits?
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)
Contact your local office
I am an expert in financial derivatives and quantitative finance, specializing in the pricing of options on futures and forwards. My expertise is grounded in a strong understanding of mathematical models, particularly the Black option pricing model, which is widely used in the industry to value financial derivatives.
In the context of the provided MATLAB code snippet, the optstockbyblk function is used to compute option prices on futures and forwards using the Black option pricing model. This model is named after Fischer Black, one of its developers, and is widely used for valuing European options on various underlying assets, including stocks, commodities, and futures.
Let's break down the key concepts and parameters used in the provided MATLAB code:
-
RateSpec (Interest-rate term structure):
RateSpecrepresents the interest-rate term structure, including the valuation date, start dates, end dates, interest rates, compounding method, etc.- It is created using the
intenvsetfunction.
-
StockSpec (Stock specification for underlying asset):
StockSpecrepresents the specification for the underlying asset, including volatility, asset price, dividend information, etc.- It is created using the
stockspecfunction.
-
Settle and Maturity:
Settleis the settlement or trade date, andMaturityis the maturity date for the option.
-
OptSpec (Option specification):
OptSpecis a cell array of character vectors defining the type of option, either 'call' or 'put'.
-
Strike:
Strikeis a vector representing the strike prices for the options.
-
ForwardMaturity (optional):
ForwardMaturityis an optional parameter specifying the maturity date or delivery date of the forward contract. If provided, it computes prices of forward options; otherwise, it calculates prices of future options.
-
Price:
Priceis the output representing the expected option prices, returned as a vector.
The examples provided demonstrate how to use the optstockbyblk function to compute option prices on futures and forwards for different scenarios, such as European call options on futures, options on forwards, and futures call options.
This MATLAB function is a powerful tool for derivative pricing, and its usage aligns with standard practices in quantitative finance. If you have any specific questions or if there's a particular aspect you'd like more information on, feel free to ask.
