Latest posts
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What Is a Good Sharpe Ratio? I Got 1.7 From Pure Noise
The usual answer is that above 1 is good, above 2 is excellent, and above 3 is exceptional. I generated ten thousand trading strategies with mathematically zero edge — pure noise, no signal, nothing to find — and backtested each over five years of daily data. The best one came back with a Sharpe ratio
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Why Your Correlation Matrix Is Not Positive Definite
Someone hands you three correlations. A against B is 0.9. A against C is 0.9. B against C is 0.5. Every number is between minus one and one. Every number is plausible on its own. Two assets strongly tied to a third, moderately tied to each other — nothing about that description should raise an
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What Is Value at Risk (And Why It Doesn’t Add Up)
Value at Risk is the number that sits at the top of every bank’s daily risk report, drives regulatory capital, and gets quoted in board meetings by people who could not define it. It is also not a measure of risk, in a sense that can be made precise. Here is a portfolio where splitting
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Your Volatility Surface Interpolation Creates Arbitrage
Take five market quotes for one-year options. Check them: every butterfly you can build from them costs money, so the quotes are arbitrage-free. Fit a cubic spline through the implied volatilities, which is what most desks and most textbooks do. The resulting surface contains a butterfly that costs minus one cent. A portfolio that can
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You Need 400 Years of Data to Estimate an Expected Return
A quant can measure the volatility of a stock to four decimal places from one year of intraday data. Measuring its expected return to within one percentage point takes four hundred years. Both numbers come from the same model, the same price series and the same estimator. The asymmetry is not a data problem, and
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Antithetic Variates Can Increase Your Variance
Every Monte Carlo tutorial recommends antithetic variates. Pair each draw with , average the two payoffs, and get a lower variance for free. It costs four lines of code and no thought. On a straddle, it makes things worse. Not marginally worse. To match the accuracy of plain Monte Carlo you need 1.64 times as
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Your CIR Simulation Produces Negative Rates
The Cox-Ingersoll-Ross process is the standard answer to a standard complaint about Vasicek: the short rate should not go negative, and CIR’s diffusion term shuts off the volatility as the rate approaches zero. The boundary is respected. That is the selling point. Then you discretise it, and 88% of your paths go negative. The instinct
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What Is the Feynman-Kac Theorem?
There are two ways to price a European option, and they look nothing alike. One is a **partial differential equation**: write down the Black-Scholes PDE, impose the payoff as a terminal condition, and integrate backwards through time on a grid. No randomness enters anywhere. It is deterministic numerical analysis. The other is an **expectation**: simulate
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What Is Gamma? (And Why Short Gamma Kills Slowly, Then All at Once)
Gamma is the rate of change of delta. That definition is correct, useless on its own, and hides the property that actually matters: gamma is why a hedged option book bleeds in a straight line for months and then loses a year of P&L in a week. It is a second derivative, which
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What Is the Hull-White Model?
Hull-White is what you use when Vasicek fails, and it fails for one reason: three parameters cannot reproduce today’s yield curve. Hull-White fixes exactly that, and the fix is smaller than people expect. One change. The constant long-run level becomes a **function of time** . Everything else — the Gaussian short rate, the