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# impvbyblk

Determine implied volatility using Black option pricing model

## Syntax

``Volatility = impvbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice)``
``Volatility = impvbyblk(___,Name,Value)``

## Description

example

````Volatility = impvbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice)` computes implied volatility using the Black option pricing model.```

example

````Volatility = impvbyblk(___,Name,Value)` specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.```

## Examples

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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 = '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(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

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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 date, specified as a `NINST`-by-`1` vector of serial date numbers or a date character vectors.

Data Types: `double` | `char`

Maturity date for the American option, specified as a `NINST`-by-`1` vector of serial date numbers or a date character vectors.

Data Types: `double` | `char`

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`

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`

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 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: `Volatility = impvbyblk(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice,'Limit',5,'Tolerance',1e-5)`

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`

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 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

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Expected implied volatility values, returned as a `NINST`-by-`1` vector. If no solution can be found, a `NaN` is returned.

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

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