σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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Skills›Probability
P

Probability Skill

LiveStart here

Every risk number, price and backtest is a statement about probability. This skill builds the ideas with short checks (numbers you compute, formulas you fill in, steps you put in order) and finance examples: a default screen that is mostly wrong, the standard error of a mean return, regimes as a Markov chain. Three Python topics on random variables, sampling and Monte Carlo are part of the syllabus. It ends with a code lab that tests whether a normal model fits real stock returns and how badly it misses the tails.

5 modules13 graded labs~11 hoursBeginner → Advanced
Start skill

Syllabus

13 topics · open any topic, in any order
  1. 1Sample spaces and eventsNot started35 minStart
  2. 2Conditional probability and Bayes' ruleNot started45 minStart
  1. 3Random variables and expectationNot startedRequires Python45 minStart
  2. 4Expectation and covarianceNot started45 minStart
  3. 5Common distributionsNot started55 minStart
  1. 6Law of large numbersNot started40 minStart
  2. 7Central limit theoremNot started45 minStart
  3. 8Transformations and change of variablesNot started45 minStart
  1. 9Sampling from distributionsNot startedRequires Python45 minStart
  2. 10Monte Carlo estimationNot startedRequires Python50 minStart
  1. 11Markov chainsNot started55 minStart
  2. 12Joint distributions and copulasNot started1 hrStart
  3. 13Capstone: return distributions against real tailsNot started1 hr 20 minStart

What you'll learn

  • Work with events and conditional probability, and use Bayes' rule without the base-rate mistake
  • Compute expectations, variances and covariances, including the variance of a portfolio
  • Pick the right distribution for a quantity (normal, lognormal, Student-t, Poisson) and read tail probabilities
  • Use the law of large numbers and the central limit theorem to size errors and confidence intervals
  • Model regimes with Markov chains and dependence with copulas, and test a return model against real tails

Tools you'll use

PythonNumPypandaspytest

Completion

Pass all 13 labs with a score of 70+ to complete the skill and earn the Probability for Quants badge on your profile.

0 / 130%

Prerequisites

High-school maths is enough. The three Python topics inside this skill help, but you can start without them.

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