# impvbyblk

Determine implied volatility using Black option pricing model

## Syntax

## Description

specifies options using one or more name-value pair arguments in addition to the input
arguments in the previous syntax.`Volatility`

= impvbyblk(___,`Name,Value`

)

## Examples

### Compute the Implied Volatility Using the Black Option Pricing Model

This example shows how to compute the implied volatility using the Black option pricing model. Consider a European call and put options on a futures contract with exercise prices of $30 for the put and $40 for the call that expire on September 1, 2008. Assume that on May 1, 2008 the contract is trading at $35. The annualized continuously compounded risk-free rate is 5% per annum. Find the implied volatilities of the stock, if on that date, the call price is $1.14 and the put price is $0.82.

AssetPrice = 35; Strike = [30; 40]; Rates = 0.05; 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(NaN, AssetPrice); % define the options OptSpec = {'put';'call'}; Price = [1.14;0.82]; Volatility = impvbyblk(RateSpec, StockSpec, Settle, Maturity, OptSpec,... Strike, Price,'Method','jackel2016')

`Volatility = `*2×1*
0.4052
0.3021

The implied volatility is 41% and 30%.

## 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 date

datetime array | string array | date character vector

Settlement date, specified as a `NINST`

-by-`1`

vector using
a datetime array, string array, or date character vectors.

To support existing code, `impvbyblk`

also
accepts serial date numbers as inputs, but they are not recommended.

`Maturity`

— Maturity date

datetime array | string array | date character vector

Maturity date for the American option, specified as a
`NINST`

-by-`1`

vector using a datetime array, string
array, or date character vectors.

To support existing code, `impvbyblk`

also
accepts serial date numbers as inputs, but they are not recommended.

`OptSpec`

— Definition of option

character vector with values `'call'`

or `'put'`

Definition of the option from which the implied volatility is
derived, specified as a `NINST`

-by-`1`

cell
array of character vectors with a value of `'call'`

or `'put'`

.

**Data Types: **`char`

| `cell`

`Strike`

— Option strike price

nonnegative scalar | nonnegative vector

Option strike price value, specified as a nonnegative scalar or
`NINST`

-by-`1`

vector of strike prices. Each row is
the schedule for one option.

**Data Types: **`double`

`OptPrice`

— European option price

nonnegative scalar | nonnegative vector

European option prices from which the implied volatility of
the underlying asset is derived, specified as a nonnegative scalar
or `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: **`Volatility = impvbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice,'Limit',5,'Tolerance',1e-5)`

`Limit`

— Upper bound of implied volatility search interval

`10`

(1000% per annum) (default) | positive value

Upper bound of implied volatility search interval, specified as the comma-separated pair
consisting of `'Limit'`

and a positive scalar.

**Note**

If you are using `Method`

with a value of
`'jackel2016'`

, the `Limit`

argument is
ignored.

**Data Types: **`double`

`Tolerance`

— Implied volatility search termination tolerance

`1e-6`

(default) | positive scalar

Implied volatility search termination tolerance, specified as the comma-separated pair
consisting of `'Tolerance'`

and a positive scalar.

**Note**

If you are using `Method`

with a value of
`'jackel2016'`

, the `Tolerance`

argument is
ignored.

**Data Types: **`double`

`Method`

— Method for computing implied volatility

`'jackel2016'`

(default) | character vector with values `'search'`

or
`'jackel2016'`

| string with values `"search"`

or
`"jackel2016"`

Method for computing implied volatility, specified as the comma-separated pair
consisting of `'Method'`

and a character vector with a value of
`'search'`

or `'jackel2016'`

or a string with a value of
`"search"`

or `"jackel2016"`

.

**Data Types: **`char`

| `string`

## Output Arguments

`Volatility`

— Expected implied volatility values

vector

Expected implied volatility values, returned as a `NINST`

-by-`1`

vector.
If no solution can be found, a `NaN`

is returned.

## References

[1] Jäckel, Peter. "Let's Be Rational."
*Wilmott Magazine.*, January, 2015 (https://onlinelibrary.wiley.com/doi/abs/10.1002/wilm.10395).

## Version History

**Introduced in R2008b**

### R2022b: Serial date numbers not recommended

Although `impvbyblk`

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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