Black-Scholes PDE Derivation in 4 minutes

In this video we derive the famous Black-Scholes Partial Differential Equation from scratch! There will be several videos following this tutorial, to break down some financial concepts in more depth.

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[paullynch]

Myron Scholes and Robert Merton were awarded the Noble Prize for their work in Option Pricing Theory in 1997 (not 1977). Sadly, Fischer Black passed away in August 1995 and was not awarded the Noble Prize (Nobel prizes are not awarded posthumously). PITY!!

[thetagang]

Hey your content is amazing. Just save the background music for next time though

[Chandra_Sekhar_T]

Small update - the final equation has sigma, not alpha. Little typo

[jianingzhuang]

Good video, but I am confused at 2:55. Why sigma square becomes alpha square?

[commonmancrypto]

I have a question I'm hoping someone can answer. Is there a specific term describing an out of the money call option whose strike price is an equal distance between the break even and the spot price? I've been calling it The equal ratio, but I thought there might be another term for it.

Keep in mind, I do not have the expertise to back any of the up, but it seems to me this equal ratio tells us something about the implied volatility of the stock going forward. For example, on certain leveraged ETFs that track indexes like the S&P and the nasdaq, the premium you get from an equal ratio out of the money call expiring in a week is as high as 4 or even 5%. By contrast, the premium you would get from a similar contract on SPY may only be 1%.

Obviously more volatile stocks will have higher implied volatility. Over time, this ratio will fluctuate, and I believe it gives us some insight into the implied volatility going forward.

[steez]

Where did alpha^2 come from in this equation at 2:58. I have sigma^2 * (S_t)^2 instead of alpha^2 * (S_t)^2.

[allensu]

I’ll pretend I understand what this means

[cookrileyw]

Honestly, not the best explanation on fundamentally why one would assume the assumptions and transformations the as described. You have merely explained how one takes said assumptions and gets the result of the the Black-Scholes equation. However, it is not remotely clear why one would do such operations to each term nor why the underline assumptions are correct or good enough. If I had no intention of understanding the mindset and implication of the B-S formula then what is the point of understanding a series of what appear to be, do to a lack of an explanation, arbitrary manipulations to arbitrary assumptions.

[sakuranooka]

@2:09 In the quadratic term, why is the mixed partial, D2C / Dt DS missing?

[DmitriiShinkevich]

Not sure in this derivation, because I have not seen that (dW)^2 == dt, it does not seem to be true in general, it's expected value of dW is, that is E[dW^2] = dt - that's true, but this is not the same right? What does the author think about this?

[sakuranooka]

@1:28 As alpha depends on t, why isn't dV_t = dC_t - a_t dS_t - da_t S_t, using the product rule?