Executive Summary
By comparing the volatility we can analyze how tightly the stock index prices are bunched around the current price. The standard deviation tells us about the potential percentage move and the dollar move these stocks may take by a certain date.
In our analysis, we have concluded that:
The higher the volatility, the bigger the standard deviation.
The further the future date, the bigger the standard deviation.
This is due to the fact that standard deviation measures the statistical dispersion, measuring how widely spread the values in a data set are. ATM option calls/put that have shorter expiration reflect smaller standard deviation, as it reflects the low volatility of the stock price, in other words, shorter expiration dates give a shorter range in which the stock price can have a positive or negative movement. For instance, ATM calls for 1-week expiration date volatility is only 2% as opposed to ATM 1 year calls having a 13.82% volatility. Thus the larger horizon is reflected in the larger probability in which the stock price will appreciate or depreciate.
In addition with SPY 168.91 and 1 week expiration date has a standard deviation of 3.38. This means that 68% of the time, the index will be 168.91 +/- 3.38. We have also concluded that ATM put and calls do not differ in volatility, since stock is equal to strike price. In this manner, mean = strike price, which means that deviation from the lose and win are the same or 50-50.
Q1.
a. The implied volatility for the ATM call option and put option with 1-week expiration are 3.38 and 3.11 respectively.
b. The implied volatility for the ATM call option and put option with 4-week expiration are 6.16 and 6.05 respectively.
c. The implied volatility for the ATM call option and put option with a 4 month expiration are 12.38 and 14.70 respectively.
d. The implied volatility for the ATM call option and put option with 1-year...