The Math of "The Trillion Dollar Equation" скачать в хорошем качестве

The Math of "The Trillion Dollar Equation"

A deep dive into Veritasium's    • The Trillion Dollar Equation   . Detailed explanation of the classic "Delta Hedging" derivation of the Black-Scholes Partial Differential Equation for European Call Options from scratch. Here are my notes from I was a PhD student on this stuff (we were allowed to bring in short notes to the exam) http://www.math.toronto.edu/mnica/PDE... http://www.math.toronto.edu/mnica/Sto... 0:00 The Trillion Dollar Equation 0:18 Veritasium's Example of the Call Option 2:13 The function v(s t) for the value of the option 3:29 Veritasium's Delta hedged portfolio 4:19 Veritasium's slide by derivation 5:24 Derivation of the Black-Scholes equation from scratch 8:26 Change in portfolio value d Pi t 9:47 Approximate changes by derivatives of v a la Taylor series 15:08 Model for the stock price S t Geometric Brownian Motion 19:42 d S t squared is just a dt a la Itos Lemma 25:44 Set delta to di v di s to perfectly hedge 27:23 Equate to the risk free interest rate equation 29:10 But isnt delta a function of time? Why does this work?