Behaviour of THETA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

The following is the behavior of Theta in relation to Time to Expiration:For ATM option, Theta increases as an option gets closer to the expiration date.On the other hand, for ITM & OTM options, Theta decreases as an option is approaching expiration.The above effects are particularly observed in the last few weeks (about 30 days) before expiration.Using the same past actual data as shown in the previous post on the behavior of Delta, namely:Options...

Read More

Behaviour of GAMMA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

As discussed previously in the earlier post, here is the behavior of Gamma in relation toTime to Expiration:Assume all other factors unchanged:For ATM options, Gamma increases (is higher) as time to expiration is nearing.In contrast, for both deep ITM and deep OTM options, Gamma normally decreases (is lower) as time to expiration is nearing.We will use the same past actual data as shown in the previous post on the behavior of Delta, namely:Options...

Read More

Behaviour of DELTA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

The following is the behavior of Delta in relation to Time to Expiration:Assume all other factors unchanged:As the time to expiration is nearing, the Delta of ITM options increases (i.e. ITM option’s Delta gets closer to 1 for Calls or to -1 for Puts) and the Delta of OTM options decreases (i.e. OTM option’s Delta gets closer to 0).Now, let’s observe using the past real data.The following is the Options Chain for Call options of RIMM as at 3 Sep...

Read More

Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS

The past articles in this blog have discussed many times about the effect of time remaining to expiration and IV on Options Greeks. In fact, not only this blog, many other websites have done the same too. Nevertheless, generally these topics are only discussed qualitatively, as it is quite tedious and time consuming to show these using real data. While there is an adage “A picture speaks a thousand words”, I am trying to show how Options Greeks behave in relation to the changes in time remaining to expiration or Implied Volatility (IV) by using...

Read More

Historical Volatility – Part 7: Comparing HV

Go back to Part 6: Interpretation.One other way to use the HV data is by comparing the values among different stocks, as well as for a particular stock.Here are some of the possible ways and its purpose/use:1) Comparing the HVs among different stocks.Although the volatility always fluctuates, it tends to oscillate around some “normal” value over long period of time, which can be deemed as its “average” value. When the volatility is relatively high or low, it would then move back or reverse towards its average value.Therefore, we can use the average...

Read More

Historical Volatility – Part 6: Interpretation

Go back to Part 5: How To Annualise Standard Deviation. After we know the definition and how to calculate HV, we’ll move on to its interpretation. Example: If it is known that the value of HV is 35%. Remember that this HV value is annualised, i.e. for one year. As mentioned in the earlier post, assuming that price returns are normally distributed, about two-third of the time, an individual return would fall within one standard deviation of the...

Read More

Historical Volatility – Part 5: How To Annualise Standard Deviation

Go back to Part 4: Understanding Standard DeviationAs mentioned earlier, Historical Volatility is actually a standard deviation. The standard deviation can be calculated using historical price data in terms of daily, weekly, monthly, quarterly or yearly.Historical Volatility is then expressed in terms of annualised standard deviation of % price returns, so that it can be compared across different stocks, regardless of the stock price and period used...

Read More

Historical Volatility – Part 4: Understanding Standard Deviation

Go back to Part 3: Steps to Calculate HV using MS Excel (with Example)As Historical Volatility (HV) is calculated using standard deviation, it might be good to understand better about the concept of standard deviation, so that we can interpret the meaning of HV better.Standard deviation is a measure of data variability or dispersion (i.e. how spread out the data points from its mean).When the standard deviation is low, that means the data points...

Read More