We developed formula on how to calculate price of PUT or CALL under uniform distribution Mean absolute deviation of a random variable is the expected value of the distance from the mean MAD - EST-E(S.T) The mean of S.T or E(S.T) is (UL)/2 The max distance from the mean is 1/2 of the full range, le 1/2" (UL) The min distance from the mean is when the random variable falls right at the mean The mean distance from the mean, le the MAD, is ]/2 of the max distance, or 1/4 of the full range for a uniform distribution: MAD - (UL) / 4 If underlying price is SO (assuming f0%), and has a mean absolute deviation (MAD) of M, then the range of underlying distribution at expiration is |LUL where L is the lower bound L=SO-2 M, and is the upper bound U-S0 2M If X is the strike, then we can derive a price for the PUT or CALL as a function of SO and M. A PUT has probability of expiring ITM of (X-L)/(UL) - (X-SO+2M)/(4'M) avg Option PMT of (X-L)/2 = (X-S0+2'M)/2 I. PUT price. (X-S0+2M)^2/(M) A CALL has probability of expiring ITM of (UX)/(UL) - (S0 X+2*M) / (4M) llavg Option PMT of (UX)/2 + (SO-X+2"M)/2 CALL price (SO-X+2M) 2/(M) 01. Option Price vs Strike Price Keep 80-100 and MAD - 25 Create a spreadsheet to Q1a. calculate PUT price, PUT intrinsic vs time value, while varying from 50 to 150 with $1 increment Q1b. calculate CALL price, CALL intrinsic vs time value, while varying X from 50 to 150 with $1 increment Q1c. Graph PUT price and intrinsic value from Q1a x-axis is X 01d. Graph CALL price and intrinsic value from Q1b.x-axis is X We developed formula on how to calculate price of PUT or CALL under uniform distribution Mean absolute deviation of a random variable is the expected value of the distance from the mean MAD - EST-E(S.T) The mean of S.T or E(S.T) is (UL)/2 The max distance from the mean is 1/2 of the full range, le 1/2" (UL) The min distance from the mean is when the random variable falls right at the mean The mean distance from the mean, le the MAD, is ]/2 of the max distance, or 1/4 of the full range for a uniform distribution: MAD - (UL) / 4 If underlying price is SO (assuming f0%), and has a mean absolute deviation (MAD) of M, then the range of underlying distribution at expiration is |LUL where L is the lower bound L=SO-2 M, and is the upper bound U-S0 2M If X is the strike, then we can derive a price for the PUT or CALL as a function of SO and M. A PUT has probability of expiring ITM of (X-L)/(UL) - (X-SO+2M)/(4'M) avg Option PMT of (X-L)/2 = (X-S0+2'M)/2 I. PUT price. (X-S0+2M)^2/(M) A CALL has probability of expiring ITM of (UX)/(UL) - (S0 X+2*M) / (4M) llavg Option PMT of (UX)/2 + (SO-X+2"M)/2 CALL price (SO-X+2M) 2/(M) 01. Option Price vs Strike Price Keep 80-100 and MAD - 25 Create a spreadsheet to Q1a. calculate PUT price, PUT intrinsic vs time value, while varying from 50 to 150 with $1 increment Q1b. calculate CALL price, CALL intrinsic vs time value, while varying X from 50 to 150 with $1 increment Q1c. Graph PUT price and intrinsic value from Q1a x-axis is X 01d. Graph CALL price and intrinsic value from Q1b.x-axis is X
