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mathdude2018
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Posts: 15
Joined: January 10th, 2018, 4:35 pm

Historical Implied Vol vs Standard Deviation for Monte Carlo Price Simulation

November 13th, 2019, 2:43 pm

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) 
Last edited by mathdude2018 on November 14th, 2019, 2:22 pm, edited 1 time in total.
 
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bearish
Posts: 5186
Joined: February 3rd, 2011, 2:19 pm

Re: Historical Implied Vol vs Standard Deviation for Monte Carlo Price Simulation

November 14th, 2019, 2:07 am

Well, the first approach only suffers from annualizing the daily standard deviation assuming independent observations, despite a pretty strong evidence of negative autocorrelation. And, of course, the use of the population standard deviation function, for no good reason. The second approach just doesn't make a whole lot of sense. At best, it involves a lot of averaging of things that can't meaningfully be averaged. But, just no.