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in this video you will learn how to use the bredon litzenberger formula to derive the risk neutral probability density functions from option prices this can be extremely useful because actual computing of option prices can be a time and computationally intensive task especially when there you have something that youre trying to do very complex dynamics of and when there is very high dimensionality the beauty of the breeden leitzenberger formula is that we can actually just compute this complicated derivatives once at different strikes for a particular tower so time to maturity and we can get this risk neutral probability distribution function and be able to calculate a whole bunch of complex derivatives extremely simply and quickly so once weve got a discrete pdf what were going to do is were going to actually use linear regression to be able to smooth out this function then were going to use a cumulative were going to create the cumulative density function and then were going