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Modules (incl. Pre-Course)
~50 lectures · 5 module exams
🗺️ Learning Journey
Pre-Course — Math Foundations
Calculus · Linear Algebra · Probability · Differential Equations
Module 1 — Building Blocks of Quant Finance
GBM · Ito's Lemma · Binomial Model · Martingales · Girsanov
Module 2 — Quantitative Risk & Return
Markowitz · VaR / CVaR · GARCH · Basel III
Module 3 — Equities & Currencies
Black-Scholes · Greeks · Exotics · Monte Carlo · Local Vol
Module 4 — Fixed Income & Commodities
Duration · Vasicek/CIR · HJM · SABR · LMM · Energy
Module 5 — Credit Products & Risk
Merton · CDS · Intensity Models · CVA/DVA/FVA · CDOs
Module 6 — Electives & Final Project
Advanced Portfolio · Heston · Rough Vol · LMM+CVA Project
💡 Beginner Study Tips
📌 Do the Pre-Course first. Ito's Lemma is a stochastic Taylor expansion — if you don't know Taylor series, it won't click.
📌 Module 1 is the spine. Every later module references stochastic calculus. Spend extra time here.
📌 Use Annotated PDFs first, then attempt the Blank version from memory.
📌 Every lecture has an Exercises PDF. Solutions are provided — do them, don't just read them.
📌 Quiz ≥ 70% before moving on. Use the Mock Exam section to test retention.
⏱️ 8-Week Schedule
Week 1: Pre-Course — all 4 Math Primer topics
Week 2: Module 1 — Stochastic Calculus (L1–L9)
Week 3: Module 2 — Portfolio Theory & Risk
Weeks 4–5: Module 3 — Black-Scholes, Exotics, Numerics
Week 6: Module 4 — Fixed Income & Rates
Week 7: Module 5 — Credit Risk
Week 8: M6 + Full Mock Exams + Revision
Click 📄 Lecture, 📝 Exercises or ✅ Solutions to open the PDF directly. Check each day when done.
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PREMath Foundations — The Toolkit
Everything in the CQF uses these four areas. Weak foundations here will slow you down in every module. One week is enough to build solid footing.
📍 Calculus
Chain Rule: d/dx[f(g(x))] = f'(g) · g'(x). Essential for Ito's Lemma (stochastic chain rule). Practice: d/dx[e^{x²}], d/dx[ln(sin x)].
Taylor Expansion: f(x+h) ≈ f(x) + hf'(x) + ½h²f''(x) + ... Ito's Lemma keeps the second-order term because (dW)² = dt is not negligible. In regular calculus h²→0 so the term drops — not here.
Gaussian integral: ∫_{-∞}^{∞} e^{-x²/2} dx = √(2π). This is how N(d₁) and N(d₂) in Black-Scholes are computed.
📍 Linear Algebra
Matrix multiplication: Portfolio return E[R_p] = wᵀμ; portfolio variance σ²_p = wᵀΣw. The covariance matrix Σ is symmetric positive semi-definite.
Eigendecomposition: Σ = QΛQᵀ. In yield curve PCA, the first eigenvector = parallel shift, second = slope, third = curvature. These explain >99% of curve moves.
📍 Probability & Statistics
Normal distribution: N(μ,σ²). CDF = N(x), PDF = n(x) = (1/√2π)e^{-x²/2}. These appear directly in B-S: N(d₁), N(d₂).
Conditional Expectation: E[X|ℱ_t] is the cornerstone of derivative pricing: V(t) = e^{-rT} E^Q[Payoff | ℱ_t].
Tower Property: E[E[X|Y]] = E[X]. Used to prove martingale properties and iterated expectations in multi-period models.
📍 Differential Equations
ODEs: dy/dx = ky → y = Ce^{kx}. The mean-reverting ODE dy = κ(θ-y)dt has solution y(t) = θ + (y₀-θ)e^{-κt}. Recognise this in Vasicek expected value.
Heat Equation: ∂u/∂t = ½σ²∂²u/∂x². The BS PDE transforms into this via x=ln(S). Its solution (Gaussian kernel convolution) gives the Black-Scholes formula.
M1Building Blocks of Quant Finance — 9 Lectures
The mathematical engine. Master Ito's Lemma and change-of-measure here and every other module will feel like a natural extension.
📍 L1 — Random Behaviour of Assets
Log-returns: r_t = ln(S_t/S_{t-1}). Additive over time, approximately normal for short Δt. Preferred over simple returns for stochastic modelling.
Wiener Process W(t): W(0)=0; W(t)-W(s) ~ N(0,t-s); independent increments; continuous paths. The fundamental "noise" driving all diffusion models.
GBM: dS = μS dt + σS dW. S stays positive. log(S) is normal → S is lognormal. Solution: S(t) = S₀ exp[(μ-σ²/2)t + σW(t)].
dS = μS dt + σS dW
S(t) = S₀ · exp[(μ - σ²/2)t + σW(t)]
E[S(t)] = S₀ eᵘᵗ, Var[S(t)] = S₀²e^{2μt}(e^{σ²t}-1)
📍 L2 — PDEs & Transition Density Functions
Fokker-Planck (forward equation): ∂p/∂t = -∂(μSp)/∂S + ½∂²(σ²S²p)/∂S². Describes how the pdf of S evolves forward in time.
Kolmogorov backward equation: Complementary view: given terminal condition, evolve backwards. The BS PDE is of this type.
Heat equation link: Substitute x=ln(S), τ=T-t into BS PDE → classical heat equation ∂u/∂τ = ½σ²∂²u/∂x² → solution via Gaussian convolution → BS formula.
📍 L3-L4 — Ito's Lemma & Stochastic Calculus
Quadratic variation rules (memorise): (dW)² = dt, dW·dt = 0, (dt)² = 0. These are the heart of stochastic calculus.
Ito's Lemma: if dS = a dt + b dW and f = f(S,t) then
df = [∂f/∂t + a·∂f/∂S + ½b²·∂²f/∂S²] dt + b·∂f/∂S dW
↑ Ito correction term (vanishes in ordinary calculus)
Key application: f = ln(S) under GBM (a=μS, b=σS): d(lnS) = (μ-½σ²)dt + σdW. Integrate → GBM solution. The -½σ² drift correction is the Ito term.
Ito integral: ∫₀ᵀ f(t)dW(t). Evaluated at left endpoint (non-anticipating). Zero mean: E[∫f dW]=0. Isometry: E[(∫f dW)²] = E[∫f² dt].
📍 L5 — Products & Strategies
Call payoff: max(S_T-K,0). Put payoff: max(K-S_T,0). Put-Call Parity (model-free): C - P = S - Ke^{-rT}.
Straddle: Long C + Long P (same K,T). Profits from large moves either direction — a bet on high realised vol.
Bull spread: Long call K₁, short call K₂ (K₁<K₂). Capped upside, capped cost. Net premium < outright call.
📍 L6 — Binomial Model (CRR)
u = e^{σ√Δt}, d = 1/u = e^{-σ√Δt}
p* = (e^{rΔt} - d)/(u - d) [risk-neutral probability]
V(node) = e^{-rΔt}[p*·V_up + (1-p*)·V_down]
As steps → ∞ and Δt → 0, binomial price converges to Black-Scholes. The model is a discrete approximation to GBM.
📍 L7-L8 — Martingale Theory
Martingale: E[M_t | ℱ_s] = M_s ∀s≤t. Brownian motion is a martingale. So is e^{σW(t)-½σ²t} (exponential martingale).
Girsanov's theorem: Change drift of BM by changing measure. Under ℚ with dℚ/dℙ = exp(-θW_T - ½θ²T): W̃_t = W_t + θt is a ℚ-Brownian motion. Used to go from real-world drift μ to risk-free drift r.
Market price of risk: θ = (μ - r) / σ
Under ℚ: dS = r·S dt + σ·S dW̃
Pricing: V(t) = e^{-r(T-t)} · E^Q[Payoff | ℱ_t]
M2Quantitative Risk & Return — 7 Lectures
Portfolio theory, risk measurement and regulatory frameworks. The practical side of quant finance.
📍 L1-L2 — Portfolio Theory & Optimisation
Markowitz Mean-Variance: Rational investors maximise E[R] for given σ or minimise σ for given E[R]. The Efficient Frontier is the set of such optimal portfolios.
Portfolio variance: σ²_p = wᵀΣw = Σᵢ Σⱼ wᵢwⱼρᵢⱼσᵢσⱼ. Diversification reduces risk when ρ < 1.
Min wᵀΣw s.t. wᵀμ=μ*, wᵀ1=1
Sharpe Ratio = (E[Rₚ] - rᶠ) / σₚ
CAPM: E[Rᵢ] = rᶠ + βᵢ·(E[Rₘ]-rᶠ), β = Cov(Rᵢ,Rₘ)/Var(Rₘ)
📍 L3-L4 — Basel III & Capital Regulation
Capital ratios: CET1 ≥ 4.5%, Tier 1 ≥ 6%, Total ≥ 8% of Risk-Weighted Assets. Banks must hold capital buffers against unexpected losses.
Leverage ratio: Tier 1 / Total Exposure ≥ 3%. A simple backstop that can't be gamed by assigning zero risk weights.
📍 L5 — VaR & Expected Shortfall
Parametric VaR: VaR_α = μ - z_α·σ. At 99%: z≈2.326. At 95%: z≈1.645. Assumes normality — underestimates fat-tail losses.
Expected Shortfall (CVaR): E[loss | loss > VaR]. Coherent — satisfies sub-additivity (diversification always reduces risk). VaR fails this. Basel IV adopts ES over VaR.
Parametric VaR_α = -μ + z_α·σ [z_{99%}=2.326, z_{95%}=1.645]
ES_α = μ - σ·φ(z_α)/(1-α) [φ = standard normal PDF]
📍 L6 — Stylised Facts
Fat tails: Excess kurtosis > 0. The normal distribution severely underestimates the probability of extreme moves. 5-sigma events happen far more often than once in millions of years.
Volatility clustering: |r_t| is autocorrelated even when r_t is not. ARCH/GARCH capture this. Explained by time-varying σ.
Negative skew (equities): Crashes are faster and sharper than rallies. Explains the put skew in options markets.
📍 L7 — ARCH/GARCH Models
GARCH(1,1): σ²_t = ω + α·ε²_{t-1} + β·σ²_{t-1}
ω = long-run component, α = shock sensitivity, β = vol persistence
Long-run vol: σ̄² = ω/(1-α-β) [requires α+β < 1]
Typical equities: α≈0.09, β≈0.90, α+β≈0.99 (very persistent)
M3Equities & Currencies — 12 Lectures
The crown jewel. Black-Scholes derivation, Greeks, exotic options, numerical methods, and volatility modelling. Most exam questions draw from this module.
📍 L1 — Black-Scholes Model
Delta-hedge derivation: Build Π = V - ΔS. Set Δ = ∂V/∂S to eliminate the dW (random) term → Π is risk-free → dΠ = rΠ dt → BS PDE.
BS PDE: ∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S - rV = 0
Call: C = S·N(d₁) - K·e^{-rT}·N(d₂)
d₁ = [ln(S/K)+(r+σ²/2)T]/(σ√T), d₂ = d₁ - σ√T
N(d₂) = risk-neutral P(S_T > K), N(d₁) = call delta
📍 L2-L3 — Martingale Approach & Feynman-Kac
Feynman-Kac: PDE solution ↔ expectation: V(S,t) = e^{-r(T-t)} E^Q[Payoff|S_t]. Use PDE approach for analytical tractability; expectation approach for MC simulation.
Fundamental Theorem: No-arbitrage ↔ ∃ risk-neutral measure ℚ. Market completeness ↔ ℚ is unique. Under ℚ, discounted prices are martingales.
📍 L4 — Volatility
Implied vol surface: σ_imp(K,T) — the σ that matches market prices. Equity surface shows skew (higher σ for lower K) and term structure. Black-Scholes assumes flat surface.
Dupire local vol: σ_loc(S,t) = √[2(∂C/∂T + rK∂C/∂K) / (K²∂²C/∂K²)]. Exact calibration to surface. But forward vol dynamics are unrealistic.
📍 L5 & L7 — Numerical Methods
Finite differences: Discretise (S,t) grid. Explicit (forward Euler): fast, conditionally stable. Implicit (backward Euler): stable, needs tridiag solve. Crank-Nicolson: average of both, 2nd-order accurate.
Monte Carlo: Price = mean discounted payoff over N simulated paths. Error ∝ 1/√N. Antithetic variates halve variance. Control variates exploit known analytical prices.
📍 L6 — Exotic Options
Barrier: Up-and-out call: expires worthless if S reaches H. Up-and-in: activated at H. BS closed-form exists using method of images.
Asian: Payoff based on average price. Geometric avg → closed form. Arithmetic avg → MC or approximation. Cheaper than vanilla because averaging smooths randomness.
Lookback: max(S_max-K,0) or max(S_T-S_min,0). Most expensive path-dependent option.
Digital/Binary: Cash-or-nothing: pays $1 if S_T>K. Price = e^{-rT}N(d₂). Delta = very high near K near expiry (difficult to hedge).
📍 L9 — The Greeks
Δ = N(d₁) [hedge ratio, ∂C/∂S]
Γ = N'(d₁)/(Sσ√T) [rate of delta change, ∂²C/∂S²]
ν = S·N'(d₁)·√T [vega, ∂C/∂σ]
Θ = -SσN'(d₁)/(2√T) - rKe^{-rT}N(d₂) [time decay]
ρ = KTe^{-rT}N(d₂) [interest rate sensitivity]
BS PDE → Θ + ½σ²S²Γ + rSΔ - rV = 0 (Theta-Gamma tradeoff)
Key insight: Long gamma = you profit from large moves but pay theta daily. Short gamma = you collect theta but lose on big moves. This is the fundamental options P&L tradeoff.
M4Fixed Income & Commodities — 14 Lectures
Interest rates are different: they mean-revert, the full yield curve must be modelled, and multiple correlated rates exist. This module covers all major frameworks.
📍 L1 — Fixed Income Products & Duration
Zero-coupon bond: P(t,T) = e^{-r(T-t)} under flat rates. General: P(t,T) = E^Q[exp(-∫ₜᵀ r(s)ds) | ℱ_t].
Duration: Weighted-average time to cash flows. Modified duration D* = -∂P/∂y / P ≈ 5 years for a typical 10yr bond.
Convexity: C = ∂²P/∂y² / P. Price change: ΔP/P ≈ -D*Δy + ½C(Δy)². Positive convexity benefits long positions (you gain more from rate falls than you lose from rises).
Duration: D = Σ tᵢ·CF_i·e^{-ytᵢ} / P
ΔP ≈ -D*·P·Δy + ½C·P·(Δy)²
P(t,T) = A(t,T)·exp(-B(t,T)·r(t)) [affine model bond price]
📍 L2 — Short-Rate Models
Vasicek: dr = κ(θ-r)dt + σdW. Mean-reverting (κ = speed, θ = long-run mean). Affine → closed-form bond prices. Allows negative rates.
CIR: dr = κ(θ-r)dt + σ√r dW. Prevents negative rates if Feller condition 2κθ > σ² holds. Also affine. Closed-form via non-central chi-squared.
Hull-White: dr = [θ(t)-κr]dt + σdW. Time-varying θ(t) fits the initial yield curve exactly. Extension of Vasicek with perfect initial-curve calibration.
Vasicek expected rate: E[r(t)] = θ + (r₀-θ)e^{-κt} → mean-reverts to θ
Vasicek bond: P = A(t,T)·exp(-B(t,T)·r), B=(1-e^{-κτ})/κ
Feller condition (CIR rates > 0): 2κθ > σ²
📍 L5 — Heath-Jarrow-Morton (HJM)
HJM framework: Model the entire forward rate curve f(t,T). Specify σ(t,T) (vol of f) → drift μ(t,T) is determined by no-arbitrage.
HJM drift restriction: μ(t,T) = σ(t,T) · ∫ₜᵀ σ(t,s)ds. Once you choose the vol structure, the drift is fixed. Vasicek, Hull-White, Ho-Lee are all HJM special cases.
HJM: df(t,T) = μ(t,T)dt + σ(t,T)dW
No-arb: μ(t,T) = σ(t,T)·∫ₜᵀ σ(t,s)ds
Ho-Lee special case: σ(t,T) = σ (constant)
📍 L7 — SABR Model
SABR: dF = σFᵝdW₁; dσ = νσdW₂; corr(W₁,W₂)=ρ. Four parameters: β (CEV exponent), ν (vol-of-vol), ρ (correlation), σ₀ (initial vol). Hagan approximation gives closed-form σ_BS(F,K).
Why SABR? Widely used for interest rate options (caps, swaptions). Naturally generates a vol smile/skew that matches market. Easy to calibrate and interpolate.
📍 L8 — LIBOR Market Model (LMM / BGM)
LMM: Models a set of LIBOR rates {L_k(t)} directly as lognormal under their forward measures. Naturally consistent with Black's formula for caps/floors.
Why LMM? Observable market rates. Consistent with cap market conventions. The catch: simulation-based only; drift-freezing approximations needed for efficiency.
LMM: dL_k = L_k·σ_k·dW_k^{T_{k+1}} (under T_{k+1}-forward measure)
Caplet price (Black's): Cpl = δ_k·P(0,T_{k+1})·[L_k(0)N(d₁)-K·N(d₂)]
📍 L10 — Further Monte Carlo (for Rates)
Simulating rates: Under LMM, simulate each L_k with appropriate drift correction when changing numeraires (the "frozen drift" or "predictor-corrector" approximation).
Quasi-MC: Replace pseudo-random numbers with low-discrepancy sequences (Sobol, Halton). Convergence improves from O(1/√N) to O((logN)^d/N).
📍 L12-L13 — Energy Derivatives
Mean-reverting commodities: Spot prices: dS = κ(θ-S)dt + σdW (Schwartz model). Energy prices are highly seasonal and mean-reverting unlike equities.
Swing options: Give the holder the right to take multiple exercise decisions over time (common in gas/power markets). Solved by dynamic programming or Least-Squares MC.
M5Credit Products & Risk — 9 Lectures
Credit risk became central post-2008. This module covers structural models, credit derivatives, and the valuation adjustments that changed derivative pricing permanently.
📍 L1 — Structural Models (Merton)
Merton's insight: Equity = call option on firm assets: E = max(V-D,0) where V = firm value, D = debt. Default at maturity if V < D.
Risk-neutral default probability: P(default) = N(-d₂) where d₁,d₂ use V,σ_V instead of S,σ_S.
KMV model: Distance-to-Default = (ln(V/D) + (μ-½σ_V²)T)/(σ_V√T). Commercial application of Merton: widely used for corporate credit scoring.
Merton: E = V·N(d₁) - D·e^{-rT}·N(d₂) [equity = call on assets]
P^Q(default) = N(-d₂)
Distance-to-Default = [ln(V/D) + (μ-½σ²)T] / (σ√T)
📍 L2 — Credit Default Swaps (CDS)
CDS mechanics: Buyer pays periodic spread s. Seller pays (1-R)·Notional on default. Fair spread: PV(default leg) = PV(premium leg).
Bootstrapping: Extract hazard rates λ(t) from observed CDS spreads at different maturities. Your Module 5 exam assignment (CDS Bootstrapping) covers this exactly.
Survival probability: S(t) = P(τ>t) = exp(-∫₀ᵗ λ(s)ds)
Quick approximation: s ≈ λ·(1-R)
CDS spread at 5yr: s = [(1-R)·∫₀⁵ λ(t)·D(t)·S(t)dt] / [∫₀⁵ D(t)·S(t)dt]
📍 L3 — Intensity (Reduced-Form) Models
Cox process: Default arrives as a Poisson process with stochastic intensity λ(t). Even with full information, you can't predict the exact default moment — it's a surprise.
Affine intensity models: λ follows a CIR process → closed-form survival probabilities. Most tractable class for calibration.
Structural vs reduced-form: Structural = default predictable from firm value (balance sheet view). Reduced-form = default as surprise arrival (trading/pricing view). Reduced-form dominates in derivatives pricing.
📍 L4-L5 — xVA (CVA, DVA, FVA)
CVA: Price reduction for counterparty default risk. CVA = (1-R)·Σᵢ DF(tᵢ)·EE(tᵢ)·PD(tᵢ₋₁,tᵢ) where EE = Expected Exposure, PD = marginal default prob.
DVA: Your own default benefit (controversial). When your credit worsens, DVA rises — banks book a P&L gain when their own spreads widen.
FVA: Cost of funding uncollateralised positions. Debate: Hull & White argue FVA is not a pricing adjustment (shareholder vs. firm perspective).
CVA = (1-R) · Σᵢ DF(tᵢ) · EE(tᵢ) · [S(tᵢ₋₁)-S(tᵢ)]
Bilateral CVA = CVA - DVA (net credit adjustment)
xVA desk manages: CVA + DVA + FVA + KVA (capital) + MVA (margin)
📍 L6-L7 — CDOs & Correlation
CDO structure: Pool of loans/bonds → tranched by loss seniority. Equity tranche absorbs first losses (highest yield, highest risk). Senior tranche absorbs last (lowest yield, highest rating).
Gaussian copula (Li 2000): Correlate default times via a Gaussian copula with single parameter ρ. Simple but fails to capture tail dependence. Overuse in structured credit contributed to 2008 crisis.
Correlation sensitivity: Senior tranche: long correlation (defaults spread out → less likely to breach senior attachment). Equity: short correlation (high correlation → all default together).
📍 L8-L9 — Statistical Methods & Cointegration
Logistic regression for PD: P(default) = 1/(1+e^{-βᵀx}). Used to estimate default probability from firm characteristics (leverage, profitability, coverage ratio).
Cointegration: Two non-stationary series X_t, Y_t are cointegrated if X_t - αY_t is stationary. Used for pairs trading (mean-reversion strategies) and modelling long-run credit spread relationships.
M6Electives — Advanced Topics
Two electives in your repo. These are graduate-level extensions of M2 and M3.
📍 Advanced Portfolio Management
Factor Models: R = α + Σβᵢfᵢ + ε. Fama-French 3 factors: market (Rm-Rf), size (SMB), value (HML). Factor exposure decompose portfolio risk.
Black-Litterman: Bayesian combination of equilibrium returns (from CAPM) with investor views. Produces more stable, less extreme weights than Markowitz. Key formula: E[R|views] = [(τΣ)^{-1} + PᵀΩ^{-1}P]^{-1}[(τΣ)^{-1}Π + PᵀΩ^{-1}Q].
Risk parity: Each asset contributes equally to total portfolio risk. In practice: overweights bonds vs. equities. Requires leverage to match equity portfolio returns.
📍 Advanced Volatility Modelling
Heston model: dS=rSdt+√v·S·dW₁; dv=κ(θ-v)dt+ξ√v·dW₂; corr=ρ. Stochastic vol with mean-reversion. Semi-analytic pricing via characteristic function + Fourier inversion.
Variance swap: Payoff = N·(σ²_realised - K_var). Fair strike K_var = E^Q[σ²_realised] = (2/T)∫₀^∞ (1/K²)C(K)dK — replication by a log-contract. Encodes the entire vol surface.
Rough volatility: Fractional Brownian motion with Hurst exponent H≈0.1 (<<0.5). Captures the observed roughness of realised vol paths better than classical diffusion models.
🗺️ CQF Interactive Mind Map
Radial overview of the entire curriculum. Hover nodes for details. Click a module node to navigate to it. Use scroll to zoom, drag to pan.
Pre-Course
M1 Quant Foundations
M2 Risk & Return
M3 Equities & FX
M4 Fixed Income
M5 Credit Risk
M6 Electives
📋 Master Formula Reference
All key CQF formulas. Print this page or keep it open during revision.
🔵 Stochastic Calculus (M1)
GBM SDE
dS = μS dt + σS dW
GBM Solution
S(t)=S₀·exp[(μ-σ²/2)t+σW(t)]
Ito's Lemma
df=(∂f/∂t+a·∂f/∂S+½b²·∂²f/∂S²)dt+b·∂f/∂S dW
Quad. variation
(dW)²=dt, dW·dt=0, (dt)²=0
Mkt price of risk
θ=(μ-r)/σ; under Q: dS=rSdt+σSdW̃
CRR Binomial
u=e^{σ√Δt}; p*=(e^{rΔt}-d)/(u-d)
🟢 Portfolio & Risk (M2)
Port. variance
σ²_p=wᵀΣw
Sharpe Ratio
SR=(E[Rₚ]-rᶠ)/σₚ
CAPM Beta
β=Cov(R,Rₘ)/Var(Rₘ)
Param. VaR
VaR_α=μ-z_α·σ [z_{99%}≈2.33]
GARCH(1,1)
σ²_t=ω+α·ε²_{t-1}+β·σ²_{t-1}
Long-run vol
σ̄²=ω/(1-α-β)
🟡 Black-Scholes (M3)
BS PDE
∂V/∂t+½σ²S²∂²V/∂S²+rS∂V/∂S-rV=0
Call Price
C=SN(d₁)-Ke^{-rT}N(d₂)
d₁, d₂
d₁=[ln(S/K)+(r+σ²/2)T]/σ√T; d₂=d₁-σ√T
Put-Call Parity
C-P=S-Ke^{-rT}
Delta/Gamma
Δ=N(d₁); Γ=N'(d₁)/(Sσ√T)
Vega/Theta
ν=SN'(d₁)√T; Θ=-SσN'(d₁)/(2√T)-rKe^{-rT}N(d₂)
🟣 Fixed Income (M4)
Duration
D*=-∂P/∂y/P; ΔP≈-D*·P·Δy
Vasicek
dr=κ(θ-r)dt+σdW
CIR
dr=κ(θ-r)dt+σ√r dW; Feller: 2κθ>σ²
HJM drift
μ(t,T)=σ(t,T)·∫ₜᵀσ(t,s)ds
Bond price
P(t,T)=E^Q[exp(-∫ₜᵀr(s)ds)]
🔴 Credit (M5)
Survival prob
S(t)=exp(-∫₀ᵗλ(s)ds)
CDS approx
s≈λ·(1-R)
CVA
CVA=(1-R)·Σ DF(tᵢ)·EE(tᵢ)·PD(tᵢ)
Merton default
P^Q(default)=N(-d₂) [firm asset model]
🤖 NotebookLM Master Prompt
Upload your CQF lecture PDFs to NotebookLM, then paste this prompt. It instructs the AI to act as a dedicated CQF tutor with rich, structured outputs.