Compute risk-neutral prices of a contract paying an asset's return or powers thereof from traded options. Part of the IMOMBOX.
M = MOPTION2PRICE(XC,C,XP,P) M = MOPTION2PRICE(XC,C,XP,P,S0) M = MOPTION2PRICE(XC,C,XP,P,S0,DF) M = MOPTION2PRICE(XC,C,XP,P,S0,DF,N)
Given call and put strikes XC and XP, corresponding call and put prices C and P, M will return the prices of contracts paying the first four powers of the asset's future return, , where N=1..4.
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 risk neutral prices for the first three moment contracts, i.e. the contracts that pay , and .
load example; M = mOption2price(dax.XC,dax.C,dax.XP,dax.P)
M = -0.0009 0.0020 -0.0001 0.0000
For example, we find that an option that pays in 28 days from now commands a price of 0.0020.