I have a daily time series data which looks something like the following:
Date , Price , PriceReturn, Premim (strike = 30.13); max(Price - 30.13, 0)
1/1/2019 , 41 , ,10.8
1/2/2019 , 27 , -0.34 , 0
1/3/2019 , 33 , 0.222 , 2.86
1/4/2019 , 24 , -0.27 , 0
1/5/2019 , 28 , 0.166 , 0
1/6/2019 , 11 , -0.60 , 0
1/7/2019 , 12 , 0.090 , 0
1/8/2019 , 27 , 1.25 , 0
1/9/2019 , 16 , -0.40 , 0
1/10/2019 , 13 , -0.18 , 0
1/11/2019 , 36 , 1.769 , 5.86
1/12/2019 , 29 , -0.19 , 0
1/13/2019 , 49 , 0.689 , 18.8
1/14/2019 , 45 , -0.08 , 14.8
1/15/2019 , 50 , 0.111 , 19.8
1/16/2019 , 47 , -0.06 , 16.8
1/17/2019 , 30 , -0.36 , 0
1/18/2019 , 23 , -0.23 , 0
1/19/2019 , 32 , 0.391 , 1.86
1/20/2019 , 39 , 0.218 , 8.86
1/21/2019 , 45 , 0.153 , 14.8
1/22/2019 , 37 , -0.17 , 6.86
1/23/2019 , 48 , 0.297 , 17.8
1/24/2019 , 21 , -0.56 , 0
1/25/2019 , 14 , -0.33 , 0
1/26/2019 , 23 , 0.642 , 0
1/27/2019 , 19 , -0.17 , 0
1/28/2019 , 14 , -0.26 , 0
1/29/2019 , 38 , 1.714 , 7.86
1/30/2019 , 33 , -0.13 , 2.86
Using annualized returns for the price series, I get standard deviation (Volatility) as 937.7%. In excel I used the formula: =STDEV.P(C2:C31)*SQRT(252) Where in Column C I have the returns for the price series.
The second step I adopted was to take average of 30 days of prices and use that as a strike of 30.13. For each day hence I calculate the premium. E.g. for 1/2/2019, premium is max(27 - 30.13, 0) = 0. For 1/11/2019, premium is max(36-30.13,0) = 5.87. This way I get premium for each day and average premium hence becomes, 5.04 for entire month of January 2019. If I was performing calculation on December 30, 2018, the average expiration for these daily options would have been 15 days. Using these parameters, annualized IV for the premium comes out to be 207%.
The questions I have are:
(1) What is the difference between two approaches, considering both are using same data
(2) Which σ (standard deviation of returns or IV) is used for monte carlo price simulation. If I am in the world of ΔS = S × (μΔt + σϵΔt)