Rates & curves
Discounting → OIS → multi-curve → Hull–White → HJM
ACADEMY V2 · MATHEMATICS TO THE DESKLEARN THE MODEL.
LEARN THE MODEL.
CHALLENGE THE HEDGE.
A structured quantitative-finance curriculum linking derivation, Python, interactive state, market practice and macro transmission.
01 · COMPLETE FLAGSHIP TRACK
Volatility
A sequenced path through measurement, option-implied coordinates, surface construction, dynamics, calibration and hedge risk.
12DEEP · DYNAMIC STAGES
01
Measurement and estimatorsRealized volatility
foundation · LAB→02Variance risk premiumRealized vs implied
foundation · LAB→03InversionBlack–Scholes implied volatility
intermediate · LAB→04Strike geometrySmile and skew
intermediate · LAB→05Expiry geometryTerm structure
intermediate · LAB→06Flagship workbenchVolatility surface
front-office · LAB→07State-dependent diffusionLocal volatility
advanced · LAB→08Random varianceStochastic volatility
advanced · LAB→09Affine stochastic varianceHeston
front-office · LAB→10Forward smile dynamicsSABR
front-office · LAB→11Fit, stability, governanceCalibration
front-office · LAB→12Hedge geometryVega, vanna and volga
front-office · LAB→One production-grade track at a time.
Numerical finance
Monte Carlo → schemes → Fourier / COS → PDE
Risk & hedging
Greeks → P&L attribution → VaR / ES → model risk
PRESERVED KNOWLEDGE GRAPH
Explore every concept.
The existing typed catalog remains intact and now sits beneath the sequenced flagship curriculum.
Asset class
114entries in this view
⌘K Search by concept, model, instrument or tag.
Foundationsfoundation
01Random Variables
Map uncertain outcomes to measurable numerical values.
Foundationspractitioner
02Brownian Motion
The continuous-time noise behind classical diffusion models.
Foundationspractitioner
03Risk-Neutral Pricing
Value discounted payoffs under a measure that removes risk premia.
Foundationsfoundation
04Bid Ask and Mid
Separate executable sides from the midpoint used for analysis.
Foundationspractitioner
05Market Price vs Model Price
Keep observed quotes separate from calculated fair values.
Foundationspractitioner
06Streaming Quotes and Staleness
Treat market data as a timed state, not a timeless number.
Foundationsfoundation
07Reference vs Real-Time Data
Distinguish official observations, delayed feeds and executable streams.
Foundationspractitioner
08Prediction Market Probabilities
Interpret binary contract prices without treating them as certainty.
Foundationspractitioner
09Prediction Event Market Outcome and Token
Keep event, market, outcome and CLOB token identifiers distinct.
Foundationspractitioner
10Prediction Market Order Books
Read bid, ask, midpoint, spread, depth and imbalance for outcome tokens.
Foundationsfront-office
11Prediction Market Resolution and Negative Risk
Connect settlement rules, oracle resolution and linked mutually exclusive markets.
Foundationspractitioner
12Prediction Market Liquidity Open Interest and Volume
Separate trading activity, outstanding exposure and available book depth.
EQpractitioner
13Realized vs Implied Volatility
Compare measured return dispersion with option-implied volatility.
EQfoundation
14Equity Forward
Lock a future equity purchase price after funding and dividends.
EQpractitioner
15Black-Scholes
Closed-form European option pricing under lognormal diffusion.
EQpractitioner
16Greeks
Local sensitivities that translate model parameters into hedge language.
EQpractitioner
17Implied Volatility
The volatility input that makes a model reproduce a market option price.
EQpractitioner
18Volatility Smile
Strike-dependent implied volatility at a single expiry.
EQfront-office
19Volatility Surface
Implied volatility across strike and maturity.
FXfoundation
20FX Spot
The exchange rate for near-immediate delivery between two currencies.
FXfoundation
21FX Forward
A future exchange rate implied by two funding curves.
FXpractitioner
22FX Swap
Exchange currencies now and reverse the exchange later.
FXpractitioner
23Garman-Kohlhagen
Black-Scholes adapted to domestic and foreign interest rates.
FXfront-office
24FX Delta Conventions
Premium-adjusted, forward and spot delta quotation choices.
FXfront-office
25Risk Reversal
Call-minus-put volatility at matched absolute delta.
FXfront-office
26Butterfly
A convexity quote combining wing and ATM volatilities.
FXfront-office
27FX Volatility Smile
Construct an FX smile from ATM, risk reversal and butterfly quotes.
IRfoundation
28Discount Factors
Present value of one unit of currency paid at a future date.
IRfoundation
29Zero Rates
Single-period rates implied by discount factors.
IRfoundation
30Forward Rates
Rates implied today for borrowing over a future interval.
IRpractitioner
31Yield Curves
Term structures linking maturity to discounting or yield.
IRpractitioner
32OIS
Fixed-versus-compounded overnight indexed swaps.
IRpractitioner
33FRAs
Contracts fixing a future simple interest rate.
IRpractitioner
34Interest Rate Swaps
Exchange fixed coupons for floating-rate cashflows.
IRfront-office
35Curve Bootstrapping
Solve discount factors sequentially from market instruments.
COMMfoundation
36Spot vs Futures
Separate immediate physical value from exchange-traded future delivery.
COMMpractitioner
37Forward Curves
Commodity delivery prices across maturities.
COMMfoundation
38Contango
A forward curve whose later deliveries trade above nearby prices.
COMMfoundation
39Backwardation
A forward curve whose later deliveries trade below nearby prices.
COMMpractitioner
40Convenience Yield
The non-cash benefit of holding physical inventory.
COMMpractitioner
41Black-76
Option pricing on forwards under lognormal forward dynamics.
COMMfront-office
42Asian Options
Options whose payoff depends on an average price.
Frontierresearch
43Rough Volatility
Very low regularity volatility models aligned with observed short-scale behaviour.
Frontierfront-office
44AAD
Adjoint algorithmic differentiation for many sensitivities at near-constant reverse cost.
Frontierresearch
45Differentiable Pricing
Pricing systems designed for gradients across models and parameters.
Frontierresearch
46Machine Learning Surrogates
Fast learned approximations to expensive pricing maps.
Frontierresearch
47Deep Hedging
Learn hedging policies under frictions and non-quadratic objectives.
Frontierresearch
48Neural SDEs
Stochastic differential equations with learned functional components.
Frontierresearch
49Bayesian Calibration
Infer parameter distributions rather than one best-fit point.
Frontierfront-office
50GPU Monte Carlo
Parallel simulation and payoff evaluation on graphics processors.
Foundationspractitioner
51Conditional Expectation
Update expected values using the information currently available.
Foundationspractitioner
52Martingales
Processes whose conditional future value equals their current value.
Foundationspractitioner
53Change of Measure
Reweight probabilities to move between pricing numeraires.
Foundationspractitioner
54Itô Calculus
Differential calculus for stochastic processes with quadratic variation.
Foundationspractitioner
55Monte Carlo
Estimate prices and risk by simulating many model paths.
Foundationspractitioner
56Variance Reduction
Improve simulation precision without merely adding paths.
Foundationspractitioner
57Finite Differences
Approximate derivatives and solve pricing PDEs on a grid.
Foundationspractitioner
58PDE Methods
Translate no-arbitrage dynamics into boundary-value problems.
Foundationsfoundation
59Calibration Basics
Choose parameters that reconcile a model with observed instruments.
Foundationsfoundation
60Interpolation Basics
Estimate values between liquid market pillars without inventing arbitrage.
Foundationspractitioner
61Numerical Stability
Keep computed outputs reliable under finite precision and difficult inputs.
EQfoundation
62Call-Put Parity
Connect European calls, puts, forwards and discounting by no-arbitrage.
EQpractitioner
63Dividend Carry
Separate funding and distributions in equity forward value.
EQfoundation
64Historical Volatility
Estimate dispersion from a time series of past returns.
EQpractitioner
65Realized Volatility
Measure variance accumulated over an observed period.
EQpractitioner
66Term Structure
Track implied volatility across option maturities.
EQpractitioner
67Local Volatility
Infer state-dependent instantaneous variance from a vanilla surface.
EQpractitioner
68Stochastic Volatility
Model volatility itself as a random process.
EQfront-office
69Heston
Model variance as a mean-reverting square-root diffusion.
EQfront-office
70SABR
Model forward and volatility jointly for smile dynamics.
EQpractitioner
71Gamma Scalping
Monetise convexity through repeated delta rebalancing.
EQpractitioner
72Variance Swaps
Trade future realised variance against a fixed strike.
EQpractitioner
73Barrier Options
Activate or extinguish payoff when an underlying crosses a level.
EQpractitioner
74Digital Options
Pay a fixed amount when a terminal condition is met.
EQpractitioner
75American Options
Allow exercise before expiry and introduce an optimal stopping problem.
EQpractitioner
76Early Exercise
Compare continuation value with immediate exercise value.
EQpractitioner
77Volatility Arbitrage
Express relative-value views across implied and realised volatility.
FXfoundation
78Forward Points
Quote the forward-minus-spot adjustment implied by two currencies.
FXpractitioner
79ATM Conventions
Define where at-the-money sits under pair-specific FX rules.
FXpractitioner
80Premium-Adjusted Delta
Account for option premium in the hedge-ratio convention.
FXpractitioner
81Smile Construction
Turn market quote coordinates into a strike-volatility curve.
FXpractitioner
82FX Digitals
Price fixed cashflows conditional on an exchange-rate event.
FXpractitioner
83FX Barriers
Add path-dependent trigger levels to FX option payoffs.
FXpractitioner
84Dual-Currency Notes
Combine fixed-income cashflows with embedded FX optionality.
FXpractitioner
85Quanto Effects
Value an asset payoff translated at a fixed exchange rate.
FXpractitioner
86Triangular Arbitrage
Enforce consistency across three quoted currency pairs.
FXpractitioner
87Cross-Currency Basis
Measure funding dislocations not explained by covered interest parity.
IRfoundation
88Day Count Conventions
Convert calendar dates into contractual accrual fractions.
IRpractitioner
89Compounding Conventions
Translate rates consistently across simple, periodic and continuous forms.
IRpractitioner
90Multi-Curve Framework
Separate discounting from tenor-specific projection curves.
IRpractitioner
91DV01
Measure value change for a one-basis-point rate shift.
IRpractitioner
92Key-Rate Duration
Allocate curve sensitivity to selected maturity nodes.
IRpractitioner
93Carry and Rolldown
Decompose expected horizon P&L with an unchanged curve.
IRpractitioner
94Caps
Limit floating-rate payments through a strip of caplets.
IRpractitioner
95Floors
Protect minimum floating-rate receipts through floorlets.
IRpractitioner
96Swaptions
Grant the right to enter an interest-rate swap.
IRpractitioner
97Short-Rate Models
Model the instantaneous funding rate to generate a term structure.
IRpractitioner
98Hull-White
Use a mean-reverting Gaussian short rate fitted to today’s curve.
IRfront-office
99LMM
Model a family of market forward rates under linked measures.
IRpractitioner
100Convexity Adjustments
Correct linear forward intuition when payoff and discounting are nonlinear.
IRpractitioner
101Negative Rates
Handle rate distributions and quotation when strikes can cross zero.
COMMfoundation
102Storage Costs
Embed physical warehousing, insurance and financing in commodity carry.
COMMpractitioner
103Seasonality
Model recurring calendar patterns in supply, demand and forward prices.
COMMpractitioner
104Roll Yield
Measure the return from moving exposure along a forward curve.
COMMpractitioner
105Calendar Spreads
Trade relative value between delivery months.
COMMpractitioner
106Commodity Swaps
Exchange floating commodity prices for fixed contractual levels.
COMMpractitioner
107Commodity Options
Attach optionality to forwards, futures or physical indices.
COMMpractitioner
108Mean Reversion
Model commodity prices returning toward an equilibrium level.
COMMpractitioner
109Spread Options
Option the difference between related prices.
COMMfront-office
110Swing Options
Optimise repeated exercise volumes under operational constraints.
COMMpractitioner
111Weather Derivatives
Link payoffs to temperature or other weather indices.
COMMpractitioner
112Crack Spreads
Track refinery margin between crude and products.
COMMpractitioner
113Spark Spreads
Track power-generation margin between electricity and fuel.
COMMpractitioner
114Real Options
Value operational flexibility using option-pricing logic.