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# accounting for options value

Discussion in 'Options' started by clarodina, Jan 8, 2011.

1. ### clarodina

How to determine how much portion of the options value change is due to change in stk price, value erode and change in implied volatility?

The Jan 11 call price for msft fall from \$2.82 to 2.62. How to determiine how much is due to stk price change, volatility and valeue erode?

Msft stk price Msft Jan '11 26 call price
1/7/2011 28.60 2.62
1/6/2011 28.82 2.82

2. ### spindr0

It's a lotta BS, ya know?

Input first set of numbers. Decrease 1 day. Compare 1 day chg to observed change. Decide what that means.

Input 2nd set of numbers. Change to IV of first numbers. Compare 1 day change to observed change. Decide what that means.

Somewhere in there is the effect of time and IV. Time to learn how to find these things from BS... or you could look at the Greeks

4. ### clarodina

Does the options greek fully explain the change in options value?

Delta = 0.25
Theta = 0.05
Vega = 0.16

Today the greeks value for a atm call are the above and the stk xyz fall a dollar and implied volatility decrease 1%. The call value is 2.30 and yestersday value should be 2.26 because 2.30 = 2.26 + 0.25 +0.05 - 0.16? Is this a accurate method to calculate the change in the call value? Are the greeks on optionxpress theory calculated or real market value calculated?

5. ### MTE

If the stock falls by \$1, the volatiliy decreases by 1%, 1 day passes and the value is 2.30 now, then the intial value was around 2.76.

2.30
+0.25 (to account for the price drop)
+0.16 (to account for the vol drop)
+0.05 (to account for the 1 day decay)
=2.76

This is not an exact value because you also need to account for gamma (i.e. changes in delta) and second derivatives of vega (vanna and vomma), but this should be close enough.

6. ### clarodina

Would you give an illustration on accounting for gamma and vanna and vomma? Why would second derivative affect the option value? They just affect the basic greeks value

7. ### MTE

Sure. The delta is neither constant not it is a discreet variable, it changes as the price of underlying changes, and gamma represents that change. So if currently the delta is 0.25 and gamma is 0.05, for example, then as the underlying gradually drops by \$1 the delta would gradually drop by 0.05 to 0.20. Therefore, if you just use the initial delta to estimate the change in the option value then you would overestimate the change, since the change wouldn't be 0.25, but less than that.

The same principle applies to vanna (sensitivity of vega to changes in the price of the underlying) and vomma (sensitivity of vega to changes in volatility).

However, if you are looking for an approximation or if you are estimating over relatively small price changes, then using the first order Greeks is sufficient. The bigger the price change the greater the effect of the second order Greeks.

8. ### clarodina

But gamma and delta are greeks value of today. That implies the 0.05 gamma and 0.25 are derived from change of stk price versus options price and delta of yestersday to today. These values do not say how tommorrow change of option price is calculated from today delta of 0.25 and gamma of 0.05. Tomorrow delta and gamma would only calculated using today price and tommorrow price. Is this correct?

Delta = change of option price / change of stk price. Change of option price would take into account of value erode and volatility change. This implies delta value include theta and vega value and the true delta should exclude theta and vega value. Is this correct?

9. ### MTE

I'm not sure I understand what you are asking. Greeks are instantaneous measures that can be calculated at any point in time, they are not calculated from actual stock price changes. Delta does NOT include vega and theta.

The definition of delta is the change in option price given \$1 change in stock price, holding everything else constant.

10. ### clarodina

today the delta value is 0.25. does this implies that tomorrow option price would decrease 0.25 with the stk price decrease 1 dollar? what is asking is today delta value reflect how much option price change tomorrow?

#10     Jan 12, 2011
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