Latest posts

  • Why Does CIR Go Negative in Simulation? (And How to Fix It)

    You implemented the CIR model, ran a simulation, and your rates went negative — or worse, your code threw a wall of NaNs. If you’re pricing with a square-root process (CIR for rates, Heston for variance) and hitting this, you’ve run into one of the most common and most misunderstood bugs in quant implementation. The

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  • What Is a Martingale? (Explained for Quant Interviews)

    “Explain what a martingale is.” It comes up constantly in quant interviews, and it’s a question where the gap between a memorised answer and a real one is obvious to anyone listening. The memorised answer: “a process whose expected future value equals its current value.” Correct, and incomplete — it misses the single most important

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  • Why does my Monte Carlo not match Black-Scholes

    You wrote a Monte Carlo pricer, ran it against the Black-Scholes formula as a sanity check, and the numbers don’t match. This is the most common rite of passage in computational finance, and the good news is that the cause is almost always one of a short list of bugs. Here’s how to diagnose it,

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  • CVA vs DVA: What’s the Difference (and Why DVA Feels Wrong)

    “What’s the difference between CVA and DVA?” is a standard interview question with a standard answer: CVA is the cost of your counterparty defaulting, DVA is the benefit of you defaulting. Recite that and you’ve answered the question. But the good follow-up — the one that separates people who’ve thought about it from people who’ve

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  • What Is a Risk-Neutral Measure? (And Why It Matters)

    “What is a risk-neutral measure, and why is it important?” It’s one of the most common opening questions in a quant interview, and one of the most commonly fumbled. Not because candidates don’t know the definition — they do — but because the definition, recited alone, doesn’t show you understand it. This is the answer

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  • What CVA Actually Is (Explained Like on a Desk, Not in a Paper)

    CVA gets explained in one of two ways. Either it’s a formula in a paper, wrapped in enough notation that you finish no wiser about what it’s for. Or it’s a one-liner — “the market value of counterparty credit risk” — that’s technically correct and completely useless. Neither tells you what a CVA desk actually

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  • Put-Call Parity: The Free Lunch Check Every Pricer Needs

    Most of what you know about option pricing depends on a model. Black-Scholes needs lognormal returns. Heston needs its own dynamics. Every one of them can be wrong, and when they are, the prices they produce are wrong with them. Put-call parity is different. It holds without assuming anything about how the stock behaves —

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  • Black-Scholes From Scratch: The Derivation That Actually Makes Sense

    Everyone can quote the Black-Scholes formula. Far fewer can say what it is — where it comes from, why those two normal CDFs are there, and what would have to be true for it to be wrong. The formula is not a model of what stocks do. It’s the answer to a narrower and much

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  • The Change of Measure (P vs Q), Explained Without the Measure Theory

    The first time you see the Black-Scholes derivation, one thing should bother you: the stock’s expected return vanishes. You start with a stock you believe will return 12% a year, you turn the crank, and the answer depends on the risk-free rate instead. Your view on the stock — the thing you’d think matters most

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  • Monte Carlo Option Pricing in Python: A Practical Guide

    You can derive Black-Scholes on a whiteboard and still freeze the first time someone asks you to put a number on the screen. That gap — between the formula and the working price — is where most quant work actually lives. Monte Carlo is the tool that closes it. This is a hands-on walkthrough of

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