Quant Finance, Explained

Course episode nine, Wilmott chapter eight. A price is useful for

about one second; then the stock moves, a day passes, volatility

shifts. The Greeks are the sensitivities that say how the price

responds. The episode opens with the vocabulary of the value sheet:

boundary conditions (state the edges first), marching backward from

expiry, the diffusion picture in which a sharp payoff corner becomes

a smooth curve, partial derivatives (a rate of change in one

direction with the others held still), and the fact that the same

equation prices a call, a put, or an early-exercise contract with

only the edges changed. The slopes of that sheet are the Greeks.

Inputs: stock price, strike, volatility, rate, time. Outputs: delta

(the share count that hedges the option), gamma (how fast delta

changes), theta (the clock), vega (volatility), rho (the interest

rate). Run once on a three-month at-the-money call: about eight

dollars, delta fifty-four hundredths, gamma two hundredths, theta

about four cents a day, vega about twenty cents a point. The one

inside idea: every Greek is a local slope, so Greeks change as the

market moves, add across a book, and gamma and theta are locked with

opposite signs. The takeaway: ask which Greek dominates the risk of

a position right now. Ends with a prompt for your own AI model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode eight, Wilmott chapter six. Price an option that

expires in months on a stock that moves continuously. Hold the

option and sell delta shares against it; over the next instant the

slope terms cancel exactly and what is left is deterministic, the

option's time decay plus the curvature term from Ito's lemma. A

riskless portfolio must earn the risk-free rate, and setting those

equal is the Black-Scholes equation, stated in words. What fell out:

the stock's expected return never appears, only its volatility, the

continuous version of the binomial tree's lesson. From equation to

price: the payoff at expiry anchors it, and for a plain call the

answer is the Black-Scholes formula, read off the bell curve. One

rule of thumb to carry: an at-the-money short-dated call is worth

about four tenths of the stock price times volatility times the

square root of time, so a three-month call on a hundred-dollar stock

at forty percent volatility is about eight dollars. What the price

means for a desk that hedges, and where the model bends. Vocabulary:

hedge portfolio, delta, riskless over an instant, the risk-free

rate, the Black-Scholes equation, boundary condition, the

Black-Scholes formula. Ends with a prompt to take to your own AI

model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode seven, Wilmott chapter five, the first stochastic

equation you read rather than derive. A spread keeps drifting away

from some level and coming back. How fast, and is that a number?

Algebra first: tomorrow's deviation is a fraction of today's plus

noise; a fraction of nine tenths closes a gap of ten to nine, then

eight point one, then seven point three, and halves it in between

six and seven steps. A fraction of one is a random walk; above one

the gap explodes. You measure the fraction by regressing today's

deviation on yesterday's. Then the continuous version: theta is the

speed, mu is the home, sigma is the shove, and the half-life is the

natural log of two over theta, about seven days for a theta of a

tenth per day. The honesty: short half-life with small noise is

tradable, long half-life with large noise is not, and a half-life

measured on one window is a hypothesis until it holds on another.

Vocabulary: mean reversion, long-run mean, speed, half-life, spread,

stationarity, autocorrelation. Ends with a prompt to take to your own

model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode six, Wilmott chapter five, the first real calculus

episode. You hold something whose value depends on a price that

follows last episode's random walk. How does your value change when

the price jiggles? The ordinary answer, slope times the price change,

is wrong, and this episode shows why by hand: expand to second order;

on a smooth path the squared change vanishes, on a random path it is

proportional to the time step because a root-of-time change squared

is the time step itself, so it survives. That surviving curvature

term is Ito's lemma. Worked case: the logarithm of the price drifts

at mu minus half sigma squared, so a stock with ten percent drift and

forty percent volatility compounds at two percent. Why curvature is

worth money, why volatility appears squared from here on, and where a

desk that hedges a short option book lives. Vocabulary: slope,

curvature, Taylor expansion, the chain rule, Brownian motion, Ito's

lemma. Ends with a prompt to take to your own AI model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode five, Wilmott chapter four. Last episode's tree had

two prices per step; real prices take many small steps. What can we

honestly say about where a price will be? This episode builds the

answer by hand: a coin-flip walk whose typical distance grows with

the square root of the number of steps, not the number of steps,

because the flips partly cancel. Then markets: a daily volatility

becomes an annual one by multiplying by about sixteen; drift grows

with time itself, so noise dominates short horizons and drift can

show over long ones. Why a point forecast is nearly worthless while

a distribution is useful, and why three up days tell you little.

Vocabulary: return, drift, volatility, random walk, independent

increments, the bell curve, standard deviation, lognormal. The first

calculus idea of the course: the square root of time, and why it

breaks ordinary calculus on random paths. The equation on the show's

cover, stated in words. Ends with a prompt to take to your own AI model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode four, Wilmott chapter three. Price a call that expires

in one step on a stock that can only go to one of two prices. The

temptation is to weight the outcomes by how likely you think they

are. Instead we build the hedge by hand with round numbers: own half

a share against the call so the portfolio is worth the same in both

states, and the price falls out with no probability of up or down

used at all. Then the risk-neutral probability: the same price from

pretending the stock earns the risk-free rate, and why that is

bookkeeping that falls out of the hedge, not a belief. What a small

positive rate changes. From one step to a tree, and why the limit is

where the calculus begins next. Vocabulary: up and down state, the

hedge, delta, riskless portfolio, risk-neutral probability,

discounting. The last calculus-free episode. Ends with a prompt to

take to your own AI model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode three, Wilmott chapter two. You open a position that

looks complicated, an iron condor, and ask: what did I actually buy?

This episode teaches the vocabulary (option, call, put, strike,

expiry, premium, payoff versus profit, intrinsic value, in and out

of the money, long and short, spread), then the dynamic: draw a call

as a hockey stick, a short put as its mirror, stack them, and see

the condor as two credit spreads whose payoff is just the sum of the

pieces. The driving-time algebra is one line: the larger of zero and

a difference. Then the first pricing law of the show, put-call

parity, proved with the same arbitrage habit as last episode and

checked in round numbers, and what it buys you: any one of call,

put, stock, or cash can be built from the other three, so a

mispriced piece is visible. No calculus yet. Ends with a prompt to

take to your own AI model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

Course episode two, Wilmott chapter one. You want to own something

later at a price fixed today. What should that price be? Not what

you think it will be worth. This episode builds the answer from

scratch: the vocabulary (spot, forward, future, long, short,

delivery, the risk-free rate, arbitrage), then the dynamic. The

forward price is the spot price carried forward at the risk-free

rate, because any other price hands someone a riskless profit. We

walk that arbitrage in both directions in plain words, do the

driving-time algebra with round numbers, and then say honestly what

the clean rule leaves out: storage cost, income, and convenience

yield. No calculus yet, on purpose. Ends with one prompt to take to

your own AI model.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.

A five-minute declaration. How math is learned is changing: from

rigor-first, bottom-up teaching to top-down learning that starts from

a real problem, with an AI model as a patient expert. The cap on how much

math you can learn is the quality of your relationship with the model

you prompt.

This podcast is the first step in that new way. It teaches two things

for the dead time in your day: the dynamics of quantitative finance,

what moves, why, and what the calculus underneath is saying, without

the rigor; and the vocabulary a quant uses, so your time with an AI model

is spent asking sharp questions. Episodes follow the order of a quant

finance textbook, one dynamic per episode, with real trading

problems as the worked examples. Derivations and rigor live

in the show notes.

For educational purposes only; not financial, investment, tax, or

legal advice. Nothing here is a recommendation to buy or sell any

instrument. Past performance is not indicative of future results.

Nothing in this podcast is financial advice. All figures discussed are historical and for educational purposes only. Do your own research and consult a licensed professional before making investment decisions.