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...

I discuss an essential method called risk-neutral pricing method that is commonly utilized to price any European contingent claim, i.e. any contract whose pay-off is determined at the expiry.

I discuss the standard shortcut of deriving Black Scholes PDE for option pricing with a critical look at its assumptions.

I discuss a simplified, yet intuitive model of evaluating option contracts that allows us to explore further two key concepts of no-arbitrage principle and risk-neutrality. This is the binomial opt...

I provide a mathematical formulation for the concept of arbitrage in finance to derive insights on various properties of option contracts.

I talk about the concept of arbitrage in finance and its utility for pricing derivative contracts such as forwards and futures.

I discuss a nice linear algebra problem that I have encountered recently.