I am looking at the USO short AUG2008 99P(delta=0.54, gamma=0.4) long JAN2010 109P(delta=0.45, gammer=0.007) What is the underlying reason the delta of 99P is greater than 109P when 109P is deeper ITM? I know it's related to the different expiration date, but does anyone know the exact relation/reason? Right now i am about +2.5 on the trade, if my bias is oil will continue to fall should i close this out now and take the profit or wait until august expiration? If i wait until august expiration i gain the theta decay + volatility->0 from the front month, but RIGHT NOW the august 99P delta and gamma are all higher than the 109P, so if the underlying continue to go down, my profit will shrink. Thanks
Keep in mind that your options model first calculates a forward price for the underlying, then calculates the option price off that. I don't know what interest rate you're using, but since the August expires soon, the forward price is just slightly higher than the spot price. The Jan 2010 expires in 535 days, so the forward price used to calculate those options is much higher. The higher the interest rate you use, the more pronounced that effect will be. There are other factors as well, but I suspect this is the one confusing you.
The AUG2008 puts have less time till expiry. So they're more sensitive to the underlying price movements, hence the higher deltas. The JAN2010 puts have a lot of time till expiration. From now till it's expiry, the underlying could move ITM, OTM, ITM, OTM countless times, and hence, it's the underlying's price now is not as significant, because it has a longer time to expiry. Hence the lower deltas. It's like your car is 500m away from a tornado (option near expiration). The current location of the tornado is very important to you, a little move of the tornado could impact you in a big way. If your car was 500km away from a tornado, the current location and it's movement is not of immediate concern to you. It'll concern you eventually, but not as much as if your car was much nearer. You should have a plan in place of what you're going to do, before you entered the trade. I'd say take the money and think carefully of how you want to trade these things in future, before you put money on it again.
DMO, think i got it now. Below is the formula in my prog for delta using blackscholes. Are you saying instead of using the SAME underlyingPrice, use the forward price, which will be different due to the different expiration. 1) How do you calculate the forward price? is the one on wiki correct? http://en.wikipedia.org/wiki/Forward_price#Forward_Price_Formula 2) For futures (es mini). Is the forward price basically the spot price for that back month contract? For example, forward price for june put will be the spot for june contract, and forward price for the sept put will be the spot for sept contract. Or does the forward price work off the front month contract only and gets calculated like a normal stock option. thanks!! Code: public static double getDeltaPut( double underlyingPrice, double strike, int daysToExpiration, double vol, double interestRate, double dividend ) { double yearsToExpiration = DateUtils.convertDayToYear(daysToExpiration); //ignore dividend dividend = 0; if (dividend != 0) underlyingPrice = underlyingPrice * Math.exp(-dividend * yearsToExpiration); double d1 = ( MathUtils.ln( underlyingPrice / strike) + (interestRate + 0.5 * Math.pow(vol, 2) ) * yearsToExpiration ) / (vol * Math.pow(yearsToExpiration, 0.5)); double deltaPut = MathUtils.normalCDistribution(d1) - 1; return deltaPut; }
With futures options you do not calculate the forward price cause the futures price is already a forward one.
Exactly correct. As for the computer code you posted - sorry, I can't read it. But the forward price is a simple calculation - you just calculate the continuously-compounded return using your interest rate and the time to expiration, add that to the spot price, and that's the forward price.