Black–Scholes Implied Volatility Sensitivity

Article Quant Q&A · Author: Zakaria Ourad

Summary

The document presents a VBA routine that estimates European call and put prices with a Black–Scholes formula, then attempts to solve for implied volatility by iterating on volatility. A reply identifies the very small volatility step used to approximate price sensitivity as a likely source of trouble: nearby trial values can make the finite-difference calculation unreliable for the intended update.

The example is a debugging exchange, not a complete treatment of implied-volatility solvers. It does not show corrected code, diagnose other possible issues, or provide numerical tests. In particular, the reply describes the issue in terms of an initial bracket, while the supplied routine uses a finite-difference slope in an iteration; readers should treat the proposed cause as a hypothesis rather than a verified fix.

Key ideas

The code estimates implied volatility by repeatedly repricing a European option under Black–Scholes.
It approximates price sensitivity to volatility with a finite difference.
The reply suggests that an excessively small volatility increment may undermine the numerical calculation.
The exchange does not validate the diagnosis or provide a tested replacement solver.

Tags

Options Derivatives pricing Volatility Statistics

Full text

# VBA Black Scholes Implied Volatility


# VBA Black Scholes Implied Volatility












I keep getting a Implied Vol. = to my initial guess, My code is as bellow

```
Option Explicit
Option Base 0
Const EPS  As Double = 10 ^ -5
Const DELTA_VOL As Double = 10 ^ -9

Function CalcEuropeanOption(opType, S, K, v, rate, T, div)

Dim d1 As Long
Dim d2 As Long
Dim normd1 As Double
Dim normd2 As Double

d1 = (Log(S / K) + (rate - div + 0.5 * v ^ 2) * T) / (v * (T ^ 0.5))
d2 = (Log(S / K) + (rate - div - 0.5 * v ^ 2) * T) / (v * (T ^ 0.5))

normd1 = WorksheetFunction.NormSDist(d1)
normd2 = WorksheetFunction.NormSDist(d2)

If opType = "call" Then
       CalcEuropeanOption = S * normd1 * Exp(-div * T) - K * Exp(-rate * T) * normd2
    Else
       CalcEuropeanOption = -S * (1 - normd1) * Exp(-div * T) + K * Exp(-rate * T) * (1 - normd2)
    End If
End Function

Function CalcImpliedVolatility(optionType)
    Dim vol1 As Double
    Dim vol2 As Double
    Dim optval1 As Double
    Dim dtm As Long
    Dim optval2 As Double
    Dim dsigma As Double
    Dim spot As Double
    Dim strike As Double
    Dim r As Double
    Dim div As Double
    Dim optval As Double
    Dim maxIter As Integer
    Dim i As Integer
    Dim dataSheet As Worksheet
    
    Set dataSheet = ActiveSheet
    
    spot = dataSheet.Range("S").Value
    strike = dataSheet.Range("K").Value
    r = dataSheet.Range("C6").Value
    dtm = dataSheet.Range("T").Value
    vol1 = dataSheet.Range("C8").Value
    div = dataSheet.Range("div").Value
    optval = dataSheet.Range("optval").Value
    
    maxIter = 100
   
    Do
       optval1 = CalcEuropeanOption(optionType, spot, strike, vol1, r, dtm, div)
       vol2 = vol1 - DELTA_VOL
       optval2 = CalcEuropeanOption(optionType, spot, strike, vol2, r, dtm, div)
       dsigma = (optval2 - optval1) / DELTA_VOL
       
       If Abs(dsigma) < EPS Or i = maxIter Then Exit Do
          vol1 = vol1 - (optval - optval1) / dsigma
          i = i + 1
    Loop
    CalcImpliedVolatility = vol1
End Function

Sub Calculate()
    Dim dataSheet As Worksheet
    Set dataSheet = ActiveSheet
    dataSheet.Range("call").Value = CalcImpliedVolatility("call")
    dataSheet.Range("put").Value = CalcImpliedVolatility("put")

End Sub
```

## Answer by Bob Jansen (score 1)

https://quant.stackexchange.com/a/55161

I have only read your code but it seems to me that `DELTA_VOL` is way too low. This causes `vol1` and `vol2` to be very close which doesn’t ensure the value your looking for is included in the initial bracket.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.

Finite-Difference Sensitivity in Black–Scholes Implied Volatility

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