# optstockbyblk

Price options on futures and forwards using Black option pricing model

## Syntax

## Description

computes option prices on futures or forward using the Black option pricing model. `Price`

= optstockbyblk(`RateSpec`

,`StockSpec`

,`Settle`

,`Maturity`

,`OptSpec`

,`Strike`

)

**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`

.

adds an optional name-value pair argument for `Price`

= optstockbyblk(___,`Name,Value`

)`ForwardMaturity`

to
compute option prices on forwards using the Black option pricing model.

## Examples

### 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 = datetime(2008,5,1); Maturity = datetime(2008,9,1); % 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 = `*2×1*
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 $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: 1

Define 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 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 = `*2×1*
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 = 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: 1

Define 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

`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

`Price`

— Expected option prices

vector

Expected option prices, returned as a
`NINST`

-by-`1`

vector.

## More About

### 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 $$F(t,T)$$, 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 $$F(s,T)-F(t,T)$$ (this reflects instantaneous marking to market).At time

*T*, the holder pays $$F(T,T)$$ and is entitled to receive*J*. Note that $$F(T,T)$$ 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 (*S** _{T}*) at that
time, is:

For a long position: $${f}_{T}={S}_{T}-K$$

For a short position: $${f}_{T}=K-{S}_{T}$$

For more information, see Forwards Option.

## Version History

**Introduced in R2008b**

### 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.

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