Series
14 posts
A casual dive into call and put options — what they actually mean, why Black–Scholes blew the market wide open, and yes, there's a dropped-class backstory involved.
Option value splits into two pieces — intrinsic value (the profit you'd lock in right now) and time value (all that probabilistic could-happen-later stuff) — here's how they work.
Before jumping into the binomial model, we lock in put-call parity — the neat reason knowing a European call's price automatically pins down its put, and vice versa.
The one-period binomial model in a nutshell — stock goes up or down, we build a risk-free portfolio, and derive the hedge ratio Δ and call option price.
Extending the one-period binomial model to two periods — turns out it's the same trick applied twice, and the binomial weights just fall right out naturally.
We tackle the scary-looking generalized n-period binomial formula and break it down piece by piece — p, u, d, sigma notation and all.
Breaking down the one chunky difference between American and European options — early exercise — and how it flips the whole binomial pricing tree on its head.
Can't derive Black-Scholes and not even gonna try — instead we're just coding it up while taking a detour through Brownian motion and Geometric Brownian Motion.
Stumbled into a stats lecture and finally got it — turns out if you scatter enough random dots and do a little ratio math, you can actually calculate π. Wild, right?
Can't derive it (lmao), but we can totally code it up — walking through the Black-Scholes pricing formula and computing actual call and put prices.
Breaking down historical and implied volatility — what they are, why we care, and how to actually compute historical vol from weekly price data in VBA.
Flip the BS formula backwards — plug in the real market price, leave σ blank, and whatever volatility makes it work? That's implied volatility, baby.
Before we can tackle FDM and crack open the Black-Scholes PDE numerically, we need to get our differentiation fundamentals straight — so let's run through it.
Toss enough random darts at a unit square, count the ones inside the circle, and — boom — you've got π, courtesy of the Monte Carlo method and a bit of Python.