# optstockbyblk

Price options on futures and forwards using Black option pricing model

## Syntax

``Price = optstockbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)``
``Price = optstockbyblk(___,Name,Value)``

## Description

example

````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`. ```

example

````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

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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 = 2×1 1.5903 0.3037 ```

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 = '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 = 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 = '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 = 2×1 0.0535 3.2111 ```

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 = 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 = '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 ```

## Input Arguments

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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`

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`

Settlement or trade date, specified as serial date number or date character vector using a `NINST`-by-`1` vector.

Data Types: `double` | `cell`

Maturity date for option, specified as serial date number or date character vector using a `NINST`-by-`1` vector.

Data Types: `double` | `cell`

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`

Option strike price value, specified as a nonnegative `NINST`-by-`1` vector.

Data Types: `double`

### Name-Value Pair Arguments

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

Example: ```Price = optstockbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'ForwardMaturity',ForwardMaturity)```

Maturity date or delivery date of forward contract, specified as the comma-separated pair consisting of `'ForwardMaturity'` and a `NINST`-by-`1` vector using serial date numbers or date character vectors.

Data Types: `double` | `cell`

## Output Arguments

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Expected option prices, returned as a `NINST`-by-`1` vector.

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### 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 $F\left(t,T\right)$, 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 $F\left(s,T\right)-F\left(t,T\right)$ (this reflects instantaneous marking to market).

• At time T, the holder pays $F\left(T,T\right)$ and is entitled to receive J. Note that $F\left(T,T\right)$ should be the spot price of J at time T.

### 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: ${f}_{T}={S}_{T}-K$

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