@quantfinancetogo: ➡️ Quantitative Finance from Scratch, part 35: how market makers make money. The first source is the spread. Like an exchange booth, a market maker buys a little below the fair price at the bid and sells a little above it at the ask, so every trade earns half the gap whatever the stock does next. After selling a call, it buys delta shares, so small moves no longer matter. The second source comes from the other Greeks: theta is the income, because the call it owes loses value every day, and gamma is the cost, because after every big move it must buy shares high and sell them low to keep the hedge. If the stock moves exactly as much as the implied volatility in the price, income and cost cancel. If it stays calmer, the market maker earns, and if it moves more, it loses. Vega is the risk to this income, because a jump in implied volatility makes the call it owes more expensive. If a customer sells it the call instead, everything flips. The code (marketmaker.py, 16 lines) sells our call from part 33 at the ask (fair $10.45, ask $10.55, bid $10.35) and hedges it every day on 2,000 simulated years with an implied volatility of 20 %. With a real volatility of 16 % it earns $1.59 per call on average and every path ends in profit; at 20 % it earns $0.10, about the spread; at 24 % it loses $1.41 and only 0.3 % of paths end in profit. Honest notes: a simplified model with one option, daily hedging, Black Scholes prices, constant volatility, no trading costs, no dividends and no other customers. Real market makers manage many options at once and also face fees, inventory limits and jumps. #quantfinance #options #marketmaking #greeks #finance

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Thursday 29 October 2026 21:34:56 GMT