MATLAB Examples

# mOption2stat

Compute risk neutral standardized moments of an asset's return distribution from traded options. Part of the IMOMBOX.

Syntax

```S = MOPTION2STAT(XC,C,XP,P)
S = MOPTION2STAT(XC,C,XP,P,S0)
S = MOPTION2STAT(XC,C,XP,P,S0,DF)
S = MOPTION2STAT(XC,C,XP,P,S0,DF,N)
```

Given call and put strikes XC and XP, corresponding call and put prices C and P, S will return the first N standardized moments of the underlying asset's future return distribution.

Input Arguments

XC and C are column vectors of the same size with matching rows. The same holds for XP and P. If the spot asset level S0 and/or the discounting factor DF are not supplied, these will be approximated along the way. N is a column or row vector holding the required moments.

## Example: DAX Data

On 2013-SEP-20, we have observed a set of call and put option prices written on the German DAX index with maturity on 2013-OCT-18. We use this set of options to compute the first four standardized moments of the DAX' return distribution from SEP to OCT.

```load example; S = mOption2stat(dax.XC,dax.C,dax.XP,dax.P) ```
```S = -0.0009 0.0020 -1.3260 5.8702 ```

We find that the options imply a large skew to the left and a high level of leptokurtosis in the DAX return distribution. The annualized implied volatility for this one month return distribution is

```sqrt(S(2)*365/dax.daysToMaturity) ```
```ans = 0.1596 ```