Quick Question

mucki · September 28th, 2004, 7:35 pm

Hi there,I've got a quick question. I'm just reading a working paper in which the author changes from the risk neutral measure to a new measure with the numéraire "asset" being S^x. I'm not quite sure whether this is per se correct since S^x is certainly not a traded asset.Thanks in advance for your comments

exotiq · September 28th, 2004, 8:11 pm

Depending on what S and x are, S^x could be a traded asset.If S is (1 - y), and x is a number of years, then your numeraire is a bond.If S is the forward price of a stock, index, currency, ETF, etc., with liquid options (say QQQ), then replicating a contract that pays S to the power of some real number x is also quite easy (though still maybe not cheap) to trade.Is it not one of these?

mucki · September 29th, 2004, 7:51 am

Thanks for your comments. I'm considering the Leland model: dV = (eta - delta) V dt + sigma V dW, where V is the asset process of a firmThe numéraire is (V / constant) ^ x, x = f(r, delta, sigma).Certainly, we cannot argue that there are a lot of options traded on the asset value of the firm (=! firm value)Any ideas?

exotiq · September 29th, 2004, 12:54 pm

Well, Leland would argue that stock is a call on that asset, a CDS is a put, the former for which you may have options on (leading Hull to apply the Geske formula to stock options), and the latter possibly having a term structure. If you are looking to trade capital structure, I agree, liquidity is not at the level I mentioned and the "power" fomula is mostly a mathematically convinient solution to an idealized differential equation.