Compute risk neutral standardized moments of an asset's return distribution from traded options. Part of the IMOMBOX.
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.
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.
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
ans = 0.1596