Topic · Derivatives & Volatility
← All topicsPricing Models
32 articles · 6 checkpoints · 18 deeper reads · 8 reference notes
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A pricing model has knobs you cannot observe directly, like volatility. Calibration is the act of turning those knobs until the model's prices match the market's prices, so you can then use the model to price the things the market doesn't quote.
Hold an option and short exactly the right number of shares and the randomness cancels out. What is left cannot earn more than a bank deposit without creating free money, and writing that sentence down gives you the Black-Scholes equation.
Black-Scholes turns a volatility guess into a price, but the market only ever gives you a price. Getting volatility back out means solving the formula backwards, and there is no algebra that does it, only iteration.
Monte Carlo runs forward in time, but an early-exercise decision needs to know the value of waiting, which lives in the future. Longstaff-Schwartz breaks the deadlock by regressing what actually happened on simulated paths to estimate that value of waiting.
Every pricing model is wrong in some specific, knowable way, and the risk that this particular wrongness costs you real money, not the risk that the market moves, is model risk.
A Monte Carlo price wobbles, and brute force is an expensive cure, four times the paths only halves the error. Variance reduction buys the same accuracy from far fewer paths by pairing random draws and borrowing quantities whose true value you already know.
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