In this series, we are going to cover interest rates term structures, from Vasicek all the way to SABR/LIBOR, but not in the usual order. We shall cover all the necessary derivations. We already have derived most of the short rate models (Merton, Vasicek, CIR, Ho Lee, and Hull White)on the quantpie.co.uk pages, so in the meantime please familiarise yourself with the term structure math. The videos here should help with the context.
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In this playlist, we will discuss the various derivations relating to the Black Scholes model. We will start with the Delta Hedging to derive the Black Scholes' PDE. We will then use variables transformation to convert the PDE to the heat/diffusion equation. And then solve the heat equation to derive the Black Scholes' formula. We will then explore other aspects of the BS framework.