Black-Scholes implied volatility

`Volatility = blsimpv(Price, Strike, Rate, Time, Value, Limit,`

Yield, Tolerance, Class)

| Current price of the underlying asset. |

| Exercise price of the option. |

| Annualized, continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number. |

| Time to expiration of the option, expressed in years. |

| Price of a European option from which the implied volatility of the underlying asset is derived. |

| (Optional) Positive scalar representing the upper bound
of the implied volatility search interval. If |

| (Optional) Annualized, continuously compounded yield
of the underlying asset over the life of the option, expressed as
a decimal number. (Default = 0.) For example, for options written
on stock indices, |

| (Optional) Implied volatility termination tolerance. A positive scalar. Default = 1e-6. |

| (Optional) Option class (call or put) indicating the
option type from which the implied volatility is derived. May be either
a logical indicator or a cell array of characters. To specify call
options, set |

```
Volatility = blsimpv(Price, Strike, Rate, Time, Value,
Limit, Yield, Tolerance, Class)
```

using a Black-Scholes model
computes the implied volatility of an underlying asset from the market
value of European call and put options.

`Volatility`

is the implied volatility of the
underlying asset derived from European option prices, expressed as
a decimal number. If no solution is found, `blsimpv`

returns `NaN`

.

Any input argument may be a scalar, vector, or matrix. When a value is a scalar, that value is used to price all the options. If more than one input is a vector or matrix, the dimensions of all non-scalar inputs must be identical.

`Rate`

, `Time`

, and `Yield`

must
be expressed in consistent units of time.

Hull, John C., *Options, Futures, and Other Derivatives*,
Prentice Hall, 5th edition, 2003.

Luenberger, David G., *Investment Science*,
Oxford University Press, 1998.

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