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Need Help With Greeks Computation

Discussion in 'Options' started by slapshot, Jan 26, 2006.

1. slapshot

Hello,

Thanks in advance to anyone who contributes in a positive, on-topic manner. Please no flamers, spammers etc. this is a serious thread for those who want to learn. You'll need your thinking caps for this one if you are on options rookie like me.

There is no need for anyone to ask strategy questions, this is merely about option valuation and modeling math.

The contract in question is a CME Euro Contract - March 06 Put, 1.1750 strike... it expires March 3rd, multiplier is 125,000

Currently the EC front month is trading @ 1.2250, so these puts are very OTM - last price today was .0009 (x 125000 = \$112.50 per contract premium)

I understand the basic ideas of Delta, Gamma, Vega and Theta as they relate to an underlying but need some help with the proper math in order to ascertain what would approximately happen if the underlying were to move .0100 in the direction of the trade and also .0100 against the trade - there are about 33 days to expiration. (in other words, EUR/USD and the EC contract have changed in price about 1 cent USD)

i.e. if the EC contract is now 1.2250 and moves to 1.2150 what should happen roughly to the price of the option which is now .0009?

... and if the EC contract goes against the put by trading up to 1.2350, what will likely happen to the price/value of the puts?

... and is there s simple way to plot the curve as the contract heads closer to ATM, such as if it moved .0300? Is there a way to plot the acceleration of contract value increase as it goes from way OTM to near ATM?

Here are the current Greeks:

Delta -0.1273

Gamma 4.6204

Vega 0.0008

Theta -0.0002

I'm sure there is some nifty software out there that can plot this stuff but I can't figure out how to make the IB analyzer work for this and besides if I can see the math then the concept will stick better...

Can anyone with substantial options experience solve my little story problem?

Perhaps this can be a great educational thread for us all.

Gratefully,

Paul

2. slapshot

Suggestions for a web site that allows for adjusting the option price and viewing the effect of/on the Greeks would be appreciated also...

3. Deringer

The delta tells how how much the option price will change, and the gamma will tell you how much delta will change.

You claimed to have basic understanding of the Greeks. So reread those parts in whatever option book you have, and you should know how to do it. They're like a chapter long, so I doubt anyone here will write every detail for you. The board is so lazy. The basic math is not really that hard. You have to at least know what a delta is. From your post, it doesn't seem like you have any familiarity with it, but you should find your answer in those pages about the greeks.

4. hopback

Delta does tell you how much the option price will move in relation to the underlying but a more realistic way of looking at it is the number of shares or % of 1 future the option currently represents.

"... and is there s simple way to plot the curve as the contract heads closer to ATM, such as if it moved .0300? Is there a way to plot the acceleration of contract value increase as it goes from way OTM to near ATM?"

you can buy software or do it yourself in excel.
you simply calculate the values at set underlying price intervals.
you can even chart them if you want pictures.
here are a few binomial formulas for puts from my excel model.

you have to provide:
-underlying price
-expiration
-todays date
-implied vol
-risk free rate
-strike
-change the multiplier (this version was set up for equities)

TV
=-((future price*delta)-(strike*((EXP(1))^(-risk free rate*((expiration-todays date)/365)))*NORMSDIST((-(((LN(future price/strike))+((risk free rate+(((implied vol/100)^2)/2))*((expiration-todays date)/365)))/((implied vol/100)*(((expiration-todays date)/365)^(1/2))))+(((implied vol/100)*(((expiration-todays date)/365)^(1/2))))))))

delta
=NORMSDIST(-((LN(future price/strike))+(((((implied vol/100)^2)*0.5)+risk free rate)*((expiration-todays date)/365)))/((((expiration-todays date)/365)^(1/2))*(implied vol/100)))

gamma
=(((EXP(1)^(-((((LN(future price/strike))+(((((implied vol/100)^2)*0.5)+risk free rate)*((expiration date-todays date)/365)))/((((expiration date-todays date)/365)^(1/2))*(implied vol/100)))^2)/2))*(1/((2*PI())^(1/2))))/(future price*(implied vol/100)*(((expiration-todays date)/365)^(1/2))))

5. slapshot

Yes, I do understand the basic concepts, but not the exact math for currency futures. The stuff I read about Greeks was based on 100 shares of stock per contract - but what I am trying to find out is do I calculate the % changes of Delta and Gamma based on EUR/USD 1.0000 or .01000 or .0010?

And how does the multiplier for each different type of FX contract change things?

6. slapshot

Thanks very much, this is helpful...

7. xtrhvydty

Also, in IB, you can plot the option price history alongside the underlying on the same chart. It's helpful to plot the bid/ask on the option chart and note how the model follows it during sudden spikes. You can even compose a combo and, without actually trading it, plot its value over several days during volatility changes. For example, the value of a DN combo can be observed during a sudden drop. It's very useful for predetermining the reliability of the option models for the particular underlying.

8. Deringer

Around 0.0003

Unless you're calculating real-time P&L of what your deltas are doing to your account, you don't really have to worry about that.

*Do the conversion afterwards to figure out the equivalent dollar value.*

ie. 0.00017 times EC multiplier.

If you don't want to calculate anything, a very simple way (yet not too accurate) to estimate is to just scan the strikes. (if you wanted to know what the 1.1750 strike put would be if EC went up 0.0100 then just check out the current price for the 1.1650 put)

Of course, there'd be a skew to whack out some numbers, but you should get a quick general ball park idea. But don't rely heavily on it. You should really use Excel or some options program.

9. ra1

Hmm, if what has been said so far is correct (see deringer's post) then it seems that a 1% increase in iv (vega +0.0008) will almost double the value of your put (from 0.0009 to 0.0017) - pretty impressive for such a tiny iv change. On the other hand theta is -0.0002, so for each passing day you lose almost 25% of your option value (0.0002), so after about 5 days your option is worth almost nothing - seems rather extreme for such a long dated option. I suspect something isn't quite right here.
ra1

10. Optionpro007

call Dr. Riskarb.

#10     Jan 27, 2006
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