# Options 101: Estimating Options Future Values Given Change in Stock Price

If you want to know what the price of an option will be based on the change in the underlying price, you can use the greeks to get an estimate. For example, if SPY goes up 5%, what will be the future value of a SPY \$440 call with 30 days to expiration, SPY price \$437.92 a delta of 0.481 and a gamma of 0.017?

Delta is the change in the price of the option given a change in the underlying price.

Gamma is the change in delta given a change in the underlying price.

Start by getting a good average delta for the entire move in the underlying. You can average the starting delta with the ending delta to get this estimate. We know the starting delta. The ending delta is the gamma * underlyingChange + delta.

Ending delta = 0.481 + gammaEffect 0.372 = 0.853

Average delta = (0.481 + endingDelta 0.853) = 0.667

deltaEffect = stockChange \$21.90 * avgDelta 0.667 = 14.61

Ending price of call = startingPrice \$7.53 + deltaEffect \$14.61 = \$22.14

Another way to think about changes in options prices when your prediction is not precise is adjusting the future distribution. If you construct a distribution of future returns based on the time to options expiration that has a zero expected value for the stock, ie. summing the percents * stock moves = 0, you can shift the future expectation to whatever your outlook is.

For example, if you think SPY will be up 5% in 30 days, the current distribution D% values the 16-May \$440 call at \$7.53. Up 5% values it at \$22.99.

You can compare the traditional approach to using delta and gamma to forecast a change in options prices to shifting the distribution. The result is close \$22.14 vs D% of \$22.99.

In summary:

\$22.14 = avgDelta .667 * stockChg 21.90 + origOption 7.53
avgDelta .667 = gamma 0.017 * stockChg 21.9

The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.

## Matt Amberson

Matt Amberson, Principal and Founder of Option Research & Technology Services. ORATS was born out of a need by traders to get access to more accurate and realistic option research. Matt started ORATS to support his options market making firm where he would hire statistically minded individuals, put them on the floor, and develop research to aid in trading options. He is heavily involved with product design and quantitative research. ORATS offers data and backtesting on a subscription basis at www.orats.com. Matt has a Master’s degree from Kellogg School of Business.