Putting It All Together
Hopefully readers can now see how different changes in assumptions (days until expiration, implied volatility, interest rates, underlying price) can have varying effects on the different Greeks and how these various inputs work together.
Below is a chart that looks at a $50 underlying product and how a range of calls and their Deltas would change given differing times until expiration and implied volatility assumptions.
Notice how implied volatility impacts Delta. With low implied volatility, in-the-money options have higher Deltas. This can be seen by referring to the 45 call vs. the 55 call highlighted in yellow below (XYZ = $50). The market does not anticipate much movement from the underlying; therefore out-of-the-money calls have relatively low Deltas. With a higher implied volatility, the same 45 call has a much lower Delta while the out-of-the-money call’s Delta increases dramatically. As the market anticipates greater price movement in the underlying, the in-the-money calls are less certain to be in-the-money at expiration.
Note too from the chart below how implied volatility has a dramatic impact on option premiums. Highlighted in orange are premiums for the 50 strike, at-the-money call options. The premiums are most dramatically impacted from rising implied volatilities for the at-the-money options. In-the-money and out-of-the-money options have lower Vega and as such, the premiums generally will not change as much when implied volatility moves compared to options with higher Vega. For this example, call premiums were used with a 3% interest rate and no upcoming dividends. And again, these figures were produced using OIC pricing calculators.
Predicting how an options premium might change in value as the different variables change is not an exact science. However by better understanding the Greeks, investors can gain insight as to how an options price may behave under a variety of conditions. Lastly, margins, taxes and commissions can and will impact any options strategy so it is necessary to keeps those costs in mind when assessing a trade.
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