But what is the forward price of GDP?
jmh: > For a first approximation you could probably just assume log changes in GDP are stationary. Yes. The important point being: GDP outperformance is followed by underperformance. GBM (and thus B-S) don’t allow this. justin: > the variance/stdev is primarily what determines the option (and warrant) price. Do you have a formula for pricing options on a mean-reverting underlier?
I doubt GDP is mean reverting. ohai Wrote: ------------------------------------------------------- > But what is the forward price of GDP? Just a guess: GDP_t = GDP_0 * e^{rt}
You could hedge by using exchange futures for the underlying country(ies)
your basis risk will be off the charts
justin88 Wrote: ------------------------------------------------------- > I doubt GDP is mean reverting. > > > ohai Wrote: > -------------------------------------------------- > ----- > > But what is the forward price of GDP? > > Just a guess: GDP_t = GDP_0 * e^{rt} Only if markets are complete. Arbitrage-free prices are pretty useless unless you can buy or sell GDP or sell it. If markets are not arbitrageable, then the forward price is simply E( GDP_t ), which would probably be something like E( GDP_t ) = GDP_0 * e^( G*t ) - 0.5*SD( G ) Where G is the long term average growth rate of the economy.
justin88 Wrote: ------------------------------------------------------- > I doubt GDP is mean reverting. In fact, it’s perhaps the single most mean-reverting financial time series you’ll ever encounter. If you’ve never looked at GDP, check e.g. http://seekingalpha.com/article/224482-the-output-gap-welcome-to-the-balance-sheet-recession e.g. That chart only goes back 30 years, it’s the same story if you go back 100 years.
I think you (and the previous person) mean that GDP growth in mean-reverting. GDP clearly has an upward trend.
you’re right, I guess I always view the world through first-differencing spectacles
DarienHacker Wrote: ------------------------------------------------------- > > Yes. The important point being: GDP > outperformance is followed by underperformance. > GBM (and thus B-S) don’t allow this. > i dont know man, in the IMF article that LPoulin133 posted they modeled real GDP using standard GBM. you would think if this was such an outrageous assumption they’ll fix this first before they jump into the other mess. of course its just a working paper so may not be publication quality
I did this years ago on the Argentina USD GDP linked warrant for a Canadian bank. There is no right or wrong way to do it, various dealers publish their methodology and each one is slightly different. The approach I used was: 1) get the real GDP growth forecast from economics department for next 5 years, put a stdev around that forecast 2) get the long term real GDP growth for the country beyond year 5, and put a larger stdev around that forecast 3) run a monte carlo based on these inputs, and simulate the country’s real GDP growth for the time horizon you need say 10,000 times 4) feed the GDP growth simulation into the warrant payout formula and discount those payouts at a risk adjusted rate (not risk free rate) to get the PV 5) now you should have a distribution of warrant values. The warrant’s fair value should be the expected value, but chances are you have skewness and kurtosis, so I always like to show the entire distribution and let the users judge
DarienHacker Wrote: ------------------------------------------------------- > If you’ve never looked at GDP, check e.g. > http://seekingalpha.com/article/224482-the-output- > gap-welcome-to-the-balance-sheet-recession e.g. > That chart only goes back 30 years, it’s the same > story if you go back 100 years. What am I supposed to be looking at here? I’m not sure whether I could tell mean reverting vs stationary just looking at one of these charts.