I explore the dynamics of mean reversion widely used in modeling interest rates in finance. Starting from basic economic intuition, I build a simple understanding of these dynamics and gradually re...

I have a closer look at the derivative pricing under the lens of Feynman-Kac theorem to (re)-discover some useful mathematical structures well known for the PDE practitioners and Statisticians

I talk about a fundamental theorem that formalize the connection between risk-neutral and PDE methods for the valuation of financial derivatives.

I construct a historical USD zero-coupon yield curve using LIBOR and par swap rates, replicating a simplified version of real-world curve bootstrapping.

From zero-coupon bonds to interest rate swaps — breaking down the math behind the money.

A gentle introduction to simple interest rate instruments and markets.

I discuss risk-neutral pricing of option contracts when the underlying stock follows a jump-diffusion process.

I explore jump diffusion models that attempt to improve the shortcomings of Black Scholes pricing theory.

I discuss conceptual issues related to Black-Scholes pricing theory and an idea to make it converge to the real world via jump diffusion processes.

I discuss the two sides of a powerful map that has important practical implications in derivative trading in the financial markets. Relying on the Fundamental theorem of Asset Pricing in finance, t...