Volatility Surface

Compute and Plot Volatility Surfaces from Market Prices

Description

The user inputs:

2 scalars:
- an annualized risk-free rate
- the current price of an underlying asset

3 vectors:
- a vector of time to maturity
- a vector of strike prices
- a vector European call prices gotten from the market for the same underlying asset.

The function VolSurface.m will then:

- compute and output the Black-Scholes implied volatility (this will be a matrix).
- get and plot the corresponding volatility surface using a kernel (Gaussian) density estimation.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Kernel Smoothing Regression

• MATLAB release: MATLAB 7.5 (R2007b)

[derivcraze R S]

If I would like to implement this code for a European Put option, do I just have to change the BS formula?

[Rodolphe Sitter]

Yes you can just modify the output of the function BlackScholesPricer so that it gives you the put price instead of the call price.
Alternatively you can convert the put prices into call prices using the put-call parity so that you don't have to modify the code.
Hope it helps

[Pankaj Kalwani]

I get the error message:

??? Error: File: C:\MATLAB6p5\work\VolSurface.m Line: 87 Column: 12
Missing operator, comma, or semicolon.

[George Tzallas]

Dear Rodolphe,

I can't understand the method you are using in order to calculate the implied volatility, ImpliedVol(i). Why you don't use newton raphson method or bisection method, in order to match the volatility with the option market price coming from the BS formula?

[Rodolphe Sitter]

Dear George,
I used the fzero command is my code which uses an algorithm originated by T. Dekker: a combination of bisection, secant, and inverse quadratic interpolation methods.
Matlab has the advantage of having a lot of built-in functions like this that you can use to make coding easier. When coding, you don't actually need to write your own algorithms but you should use the available Matlab functions who do the hard work for you.
I hope it answers you question.
thx for the feedback.

[Darren]

Dear Rodolphe,
In follow up to my previous question: More important than the graph, shouldn't the surface structure return T, M, and IV to Example 1 (once I comment out the graphing issue)? I receive empty matrices.

Output:
Elapsed time is 0.552350 seconds.
>> whos
  Name Size Bytes Class Attributes

  CallPrice 721x1 5768 double
  Maturity 721x1 5768 double
  S0 1x1 8 double
  SPX 723x4 23136 double
  Strike 721x1 5768 double
  r 1x1 8 double
  surface 1x1 636 struct

>> surface

surface =
    hT: NaN
    hM: NaN
     T: [0x2 double]
     M: [0x2 double]
    IV: [1x0 double]

[Marc]

I like the kernel smoothing part ! thks for sharing