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in the last video we already got an overview that if you give me a stock price and an exercise price and a risk-free interest rate and a time to expiration and the volatility or the standard deviation of the log returns if you give me these six things so if you give me these things six things I can put these into the black Scholes formula I can put these into the black the black Scholes formula so black Scholes formula and I will output and I will output for you the appropriate price for this European call option for this European call option so it sounds all very straightforward and some of this is straightforward the stock price is easy to look up the exercise price well that's part of the contract you know that the risk-free interest rate there are good proxies for it money market funds there's there's there's government debt things like that so that's pretty easy to figure out or at least approximate the the time to expiration well you know that you know what today's date is you know when this thing is going to expire so that's pretty straightforward but now let's think a little bit about volatility so how do you actually measure the standard deviation of log returns now one of the assumptions that about black Scholes formula is that this is a constant thing this is just some intrinsic property of this security well the only way that you can at least attempt to estimate it is by looking at the history of the standard deviation of log returns so the way that people would normally do it as well they'll say okay what has what has historically been the standard deviation of log returns over some time period where that security has not changed in some dramatic way and then use that as the input and then they would come up with some price well that's all interesting but it's very important to know that this is an estimate this right over here is an estimate there's no way of us actually knowing the actual intrinsic and it's even up for grabs whether there is whether you can even assume that there's some constant intrinsic property as this volatility that's going to be constant over the life of this option so this is just an estimate it's important to know that but what is interesting is that these things are being traded these call options are being traded all of the time and so you could actually look up the price of this call option you could look up a call option with this struck this stock price this exercise price you know what these two things are and you could say hey look this traded for three dollars just now so you actually can figure out what this is which raises another very very interesting question if you know exactly what this is because you know what or you know what the market is pricing this at so let me write this so you know what the market believes this price should be so the market believe market belief and it's based on their actual transaction so it's based on transaction so this is what the market is saying the correct price is so you can figure that out you can just look that up you can figure out all these other stuff can you then take this output plus all of these to work backwards through black Scholes to figure out what the market is guessing about this or what the market is estimating about that and the answer is yes and this is where this whole this whole idea about when people talk about what is the volatility in the market or even where is where our current volatility rates or what does the market expect volatility to be well how do we know what the market expects volatility to be well we can look at what markets are trading options at and we could look at all of this other information that would be inputted into black Scholes equation and we can say hey look based on the fact that the market is paying five dollars for this option and all of these other variables they must assume that the standard deviation of log returns for this security is now this now let's say that things get really scary the market becomes a lot Dicer and choppier well then people are going to pay more for this option it's going to drive the implied volatility up so when you hear people talk about implied volatility or implied Volland or even people who will actually trade on implied volatility so implied volatility this is what they're talking about they're saying look options are trading all the time can we use that price the market belief what those prices should be and then work backwards through black-scholes to figure out because we know these are all facts we can look these things up but based on what the market is trading these options at can we figure out what the what the implied volatility with the implied market belief about volatility for that security is and then we could actually aggregated across many many securities and come up with an implied volatility for given markets at a time so it's a very very very interesting idea but in some levels is kind of a kind of a basic one you just working backwards through black Scholes