Appendix C — Financial Glossary

Key terms used throughout this book, organised alphabetically within topic areas.

C.1 Fixed Income

Accrued Interest — The interest that has accumulated on a bond since the last coupon payment date. Dirty price = clean price + accrued interest.

Basis Point (bp) — One hundredth of one percent: 1 bp = 0.0001 = 0.01%. Yield changes, spreads, and option sensitivities are commonly quoted in basis points.

Bond — A fixed income instrument in which the issuer promises to pay periodic coupon payments and return the face value (notional) at maturity. Clean price is quoted; dirty price is paid.

Convexity — The second derivative of bond price with respect to yield, divided by price: $C = \frac{1}{P} \frac{d^2P}{dy^2}$. Positive convexity means the price gain from a yield decrease exceeds the price loss from an equal yield increase.

Coupon — The periodic interest payment of a bond, typically quoted as an annual percentage of face value and paid semi-annually.

Day Count Convention — The rule for computing the year fraction between two dates. Common conventions: Act/365 (actual days / 365), Act/360 (actual days / 360), 30/360 (each month treated as 30 days).

Discount Factor — The present value of \$1 received at a future date $t$: $DF(t) = e^{-r(t) \cdot t}$ under continuous compounding.

Duration (Modified) — The negative of the percentage price change per unit yield change: $D_{mod} = -\frac{1}{P} \frac{dP}{dy}$. Approximately: $\Delta P / P \approx -D_{mod} \cdot \Delta y$.

DV01 — Dollar Value of a Basis Point: the change in dollar value of a position for a 1 bp increase in yield. $\text{DV01} = D_{mod} \cdot P / 10000$.

Forward Rate — The interest rate implied for a future period, derived from the spot rate curve. $f(t_1, t_2)$ is the rate from time $t_1$ to $t_2$ as seen today.

Libor / SOFR — London Interbank Offered Rate (LIBOR) was the benchmark short-term unsecured lending rate between banks, now replaced by SOFR (Secured Overnight Financing Rate) following the 2021 transition.

Par Rate — The coupon rate that makes a bond price equal to its face value. The par swap rate is the fixed rate that makes a swap's NPV zero at inception.

Spot Rate (Zero Rate) — The yield on a zero-coupon bond maturing at time $t$. Also called the zero-coupon yield or zero rate. Used to build the discount curve.

Yield to Maturity (YTM) — The single discount rate that, when applied to all cash flows, gives the current market price. Implicitly assumes all coupons are reinvested at the YTM rate.

Yield Curve — The relationship between yields (or spot rates or forward rates) and maturity. Normally upward-sloping; inversions (short rates > long rates) have historically preceded recessions.

z-Spread — The parallel shift to the risk-free yield curve that equates the present value of a bond's cash flows to its market price. Measures credit and liquidity spread above the risk-free rate.

C.2 Derivatives

American Option — An option that can be exercised at any time up to and including the expiry date. More valuable than an otherwise identical European option for puts (and for calls on dividend-paying stocks).

At-the-Money (ATM) — An option whose strike equals the current underlying price ($S = K$). ATM options have the highest time value and are most sensitive to volatility.

Basel IV / FRTB — The Fundamental Review of the Trading Book, finalised under Basel III/IV. Replaced VaR with Expected Shortfall for market risk capital; introduced liquidity horizons and internal model restrictions.

Black's Model — Extension of Black-Scholes to futures and forward prices. Widely used for caps, floors, and swaptions, where the forward rate plays the rôle of the forward price.

Black-Scholes Model — The seminal 1973 options pricing model by Fischer Black, Myron Scholes, and Robert Merton. Assumes continuous log-normal asset price dynamics and derives a closed-form formula for European call and put prices.

Cap / Floor — An interest rate cap pays the holder when a reference rate exceeds a strike. A floor pays when the reference rate falls below the strike. Both are portfolios of caplets/floorlets priced with Black's formula.

Credit Default Swap (CDS) — A bilateral contract where the protection buyer pays a periodic fee (the CDS spread) and receives $(1-R)$ notional if the reference entity defaults. Functions as credit insurance.

Delta ($\Delta$) — The first derivative of option price with respect to underlying price: $\Delta = \partial V / \partial S$. Also the number of units of the underlying needed to hedge the option.

European Option — An option that can be exercised only at expiry. A European call pays $\max(S_T - K, 0)$; a European put pays $\max(K - S_T, 0)$.

Forward Contract — An agreement to buy or sell an asset at a specific price (the forward price) at a future date. The fair forward price is $F = S e^{(r-q)T}$ where $q$ is the dividend yield.

Gamma ($\Gamma$) — The second derivative of option price with respect to underlying price: $\Gamma = \partial^2 V / \partial S^2$. Long gamma profits from large moves; short gamma profits from small moves (but faces unlimited loss in crashes).

Implied Volatility — The volatility $\sigma$ that, when substituted into the Black-Scholes formula, reproduces the observed market option price. The market's forward-looking volatility estimate.

In-the-Money (ITM) — A call option is ITM when $S > K$; a put is ITM when $S < K$. ITM options have intrinsic value in addition to time value.

Intrinsic Value — The payoff if the option were exercised immediately: $\max(S-K, 0)$ for a call, $\max(K-S, 0)$ for a put.

Out-of-the-Money (OTM) — A call is OTM when $S < K$; a put is OTM when $S > K$. OTM options consist entirely of time value.

Put-Call Parity — The no-arbitrage relationship $C - P = S e^{-qT} - K e^{-rT}$ between European call ($C$) and put ($P$) on the same underlying with the same strike and expiry.

Rho ($\rho$) — The sensitivity of option price to the risk-free interest rate: $\rho = \partial V / \partial r$.

Swaption — An option to enter a specified interest rate swap at a future date. A payer swaption gives the right to pay fixed; a receiver swaption gives the right to receive fixed.

Theta ($\Theta$) — The time decay of option value: $\Theta = \partial V / \partial t$. For long options, theta is negative — options lose value as time passes, all else equal.

Vega ($\mathcal{V}$) — The sensitivity of option price to implied volatility: $\mathcal{V} = \partial V / \partial \sigma$. Long options always have positive vega.

Volatility Smile / Skew — The pattern of implied volatility varying by strike. Equity options exhibit a skew (OTM puts have higher IV than OTM calls) reflecting crash risk and the leverage effect.

Volatility Surface — The two-dimensional surface of implied volatility as a function of both strike and maturity.

C.3 Credit

CDO (Collateralised Debt Obligation) — A structured product that pools debt instruments and issues notes in tranches of different seniority (equity, mezzanine, senior). Senior tranches absorb losses last and are rated AAA; equity tranches absorb first losses but receive the highest yield.

Credit Spread — The yield differential between a corporate bond and an equivalent-maturity government bond. Reflects compensation for default risk, liquidity risk, and tax differences.

Default Probability (PD) — The probability that a borrower fails to meet its contractual obligations within a given horizon. Can be physical (historical) or risk-neutral (from market prices).

Distance to Default (DD) — In Merton's model: $DD = (\ln(V/D) + (\mu - \sigma^2/2)T) / (\sigma\sqrt{T})$, the number of standard deviations between current asset value and the default barrier.

Hazard Rate ($\lambda$) — The instantaneous conditional default probability: $P(\tau \in [t, t+dt] \mid \tau > t) = \lambda(t) \cdot dt$. Survival probability is $Q(T) = \exp(-\int_0^T \lambda(t) \cdot dt)$.

LGD (Loss Given Default) — The fraction of exposure lost when a borrower defaults: LGD = $1 - R$ where $R$ is the recovery rate. Typical bond recovery is 40 cents on the dollar.

Recovery Rate ($R$) — The fraction of face value recovered by creditors after a default. US investment-grade bonds have recovered approximately 40% on average historically.

Survival Probability — The probability that a counterparty or reference entity does not default before time $T$: $Q(T) = e^{-\lambda T}$ for constant hazard rate $\lambda$.

C.4 Risk Management

CVA (Credit Valuation Adjustment) — The market value of counterparty default risk embedded in a derivative: the price reduction applied to account for the possibility the counterparty defaults before all payments are made.

DVA (Debit Valuation Adjustment) — The symmetric adjustment for own-default risk. Controversial because it implies a profit when own credit quality deteriorates.

Expected Shortfall (ES / CVaR) — The expected loss given that the loss exceeds VaR: $ES_\alpha = E[L \mid L > \text{VaR}_\alpha]$. A coherent risk measure; required for regulatory capital under FRTB.

Market Risk — The risk of loss due to changes in market prices: equity prices, interest rates, FX rates, commodity prices, and credit spreads.

Sharpe Ratio — Risk-adjusted return metric: $SR = (R_p - R_f) / \sigma_p$ where $R_p$ is portfolio return, $R_f$ is risk-free rate, and $\sigma_p$ is portfolio volatility.

Value at Risk (VaR) — The loss not exceeded with probability $\alpha$ over horizon $h$: $P(L > \text{VaR}_\alpha) = 1 - \alpha$. E.g., 1-day 99% VaR = loss exceeded on 1% of trading days.

XVA — Collective abbreviation for valuation adjustments to derivative prices: CVA, DVA, FVA (Funding), KVA (Capital), MVA (Margin).

C.5 Stochastic Calculus

Brownian Motion (Wiener Process) — A continuous-time stochastic process $W_t$ with $W_0 = 0$, independent increments, $W_t - W_s \sim \mathcal{N}(0, t-s)$, and almost surely continuous paths.

Geometric Brownian Motion (GBM) — The standard model for equity prices: $dS_t = \mu S_t \cdot dt + \sigma S_t \cdot dW_t$. Has log-normal marginals: $S_T = S_0 \exp((\mu - \sigma^2/2)T + \sigma W_T)$.

Girsanov's Theorem — The change-of-measure result that allows removing the drift $\mu$ from GBM by shifting to the risk-neutral measure $\mathbb{Q}$. Under $\mathbb{Q}$, all assets earn the risk-free rate.

Itô's Lemma — The stochastic calculus chain rule. For $V = f(S_t, t)$: $dV = \frac{\partial f}{\partial t} dt + \frac{\partial f}{\partial S} dS + \frac{1}{2} \frac{\partial^2 f}{\partial S^2} (dS)^2$, where $(dW)^2 = dt$.

Itô Integral — A stochastic integral $\int_0^T H_s \cdot dW_s$ where $H_s$ is adapted (non-anticipating). Different from Stratonovich integral; the Itô chain rule (Itô's lemma) requires the extra $\frac{1}{2}\sigma^2$ correction term.

Martingale — A stochastic process $M_t$ with $E[M_t \mid \mathcal{F}_s] = M_s$ for $s < t$. Under the risk-neutral measure, discounted asset prices are martingales.

Risk-Neutral Measure ($\mathbb{Q}$) — The probability measure under which all discounted asset prices are martingales. Option prices equal the discounted risk-neutral expectation of the payoff: $V_0 = e^{-rT} E^{\mathbb{Q}}[\text{payoff}]$.

SDE (Stochastic Differential Equation) — An equation specifying the dynamics of a stochastic process: $dX_t = \mu(X_t, t) \cdot dt + \sigma(X_t, t) \cdot dW_t$.

C.6 Portfolio and Market Microstructure

Alpha — The component of return not explained by market beta: $\alpha = R_p - \beta R_m$. Also used loosely to mean any source of excess risk-adjusted return.

Arbitrage — A portfolio that generates a positive payoff with no initial cost and no risk. The no-arbitrage principle is the foundation of all derivatives pricing.

Beta — The sensitivity of a portfolio's excess return to the market's excess return: $\beta = \text{Cov}(R_p, R_m) / \text{Var}(R_m)$.

Efficient Frontier — The set of portfolios that offer the highest expected return for each level of variance. Introduced by Markowitz (1952).

Implementation Shortfall — The difference between the paper portfolio return (at the decision price) and the actual portfolio return (at execution prices). Measures total execution cost including spread, impact, and timing.

Market Impact — The adverse price movement caused by a trader's own order flow. Approximately proportional to $\sqrt{Q/V}$ where $Q$ is trade size and $V$ is daily volume (the square-root law).

Maximum Drawdown — The largest peak-to-trough decline in portfolio value over a specified period. A key measure of downside risk and strategy viability.

Risk Parity — A portfolio construction approach that allocates capital so that each asset contributes equally to total portfolio risk (volatility), rather than allocating equal capital weights.

Sharpe Ratio — See Risk Management section above.

Variance Swap — A contract that pays the difference between realised variance and a pre-agreed variance strike. Model-free hedge for volatility exposure; underlies the VIX index construction.

C.7 Execution and Market Microstructure

Adverse Selection — The phenomenon where informed traders systematically trade against market makers, causing the market maker to lose money on average. Motivates bid-ask spreads as compensation.

Almgren-Chriss Model — A framework for optimal execution that minimises the expected cost plus a risk penalty. The optimal strategy is a hyperbolic sine schedule that trades faster when risk aversion is high.

Bid-Ask Spread — The difference between the best ask (lowest offer) and best bid (highest bid) in the order book. Compensates market makers for inventory risk and adverse selection.

Dark Pool — A private trading venue where orders are not displayed publicly before execution. Reduces market impact for large orders but may result in worse prices due to adverse selection.

TWAP (Time-Weighted Average Price) — An execution benchmark that divides the order equally across time slices. Simple but ignores intraday volume patterns.

VWAP (Volume-Weighted Average Price) — An execution benchmark that weights execution by expected intraday volume. Outperforms TWAP when volume is predictable.

Glosten-Milgrom Model — A sequential trade model where the bid-ask spread arises from adverse selection by informed traders. The market maker updates beliefs using Bayes' rule after each trade.

Kyle's Lambda ($\lambda$) — The price impact coefficient in Kyle's (1985) model: $\Delta p = \lambda \cdot Q$ where $Q$ is order flow. Measures market depth; higher $\lambda$ means less liquid markets.

Limit Order — An order to buy or sell at a specified price or better. Provides liquidity to the market but may not execute if the price is not reached.

Market Order — An order to buy or sell immediately at the best available price. Guarantees execution but not price; incurs market impact.

Order Book — The electronic record of all outstanding limit orders, organised by price level. The best bid and ask form the inside market.

Participation Rate — The fraction of market volume that a trader's execution represents. High participation rates increase market impact.

Price Impact — The change in market price caused by a trade. Temporary impact reverts after the trade; permanent impact reflects information content.

Slippage — The difference between the expected execution price and the actual execution price. Includes spread, market impact, and timing costs.

Square-Root Law — The empirical observation that market impact scales as $\sqrt{Q/V}$ where $Q$ is trade size and $V$ is average daily volume. Supported by extensive empirical evidence.

C.8 Regulatory and Risk Framework

Basel III / IV — International banking regulations setting minimum capital requirements. Basel IV (finalised 2017, phased in 2023–2028) tightened internal model constraints and introduced the output floor.

CCAR (Comprehensive Capital Analysis and Review) — The US Federal Reserve's annual stress test for large bank holding companies. Banks must demonstrate sufficient capital under severely adverse scenarios.

DFAST (Dodd-Frank Act Stress Testing) — Mandatory stress tests for US banks with assets over $100 billion. Scenarios include severely adverse macroeconomic conditions.

FRTB (Fundamental Review of the Trading Book) — Basel Committee reform replacing VaR with Expected Shortfall for market risk capital. Introduced the Sensitivity-Based Approach (SBA) and Internal Models Approach (IMA).

IFRS 9 — International accounting standard for financial instruments. Replaced IAS 39; introduced the Expected Credit Loss (ECL) model requiring forward-looking provisioning.

Initial Margin (IM) — Collateral posted at the start of a derivatives trade to cover potential future exposure. SIMM (Standard Initial Margin Model) is the industry standard for bilateral IM calculation.

KVA (Capital Valuation Adjustment) — The cost of holding regulatory capital against a derivatives position over its lifetime. Part of the XVA framework.

MVA (Margin Valuation Adjustment) — The funding cost of posting initial margin over the life of a derivatives trade. Became significant after mandatory clearing and bilateral IM rules.

Regulatory Capital — The minimum capital a bank must hold against its risk exposures, as required by regulators. Includes Tier 1 (equity) and Tier 2 (subordinated debt) capital.

SIMM (Standard Initial Margin Model) — The ISDA industry model for calculating initial margin on non-cleared derivatives. Based on sensitivities (delta, vega, curvature) across risk factors.

Stress Testing — The process of evaluating a portfolio's performance under extreme but plausible scenarios. Regulatory stress tests (CCAR, DFAST) use macroeconomic scenarios; internal stress tests may use historical or hypothetical scenarios.

VaR (Value at Risk) — See Risk Management section. Under Basel II/III, 10-day 99% VaR was the primary market risk capital metric. FRTB replaced it with 10-day 97.5% ES.

C.9 OCaml and Functional Programming

Algebraic Data Type (ADT) — A type formed by combining other types. Sum types (variants) represent alternatives; product types (records/tuples) represent combinations. The foundation of type-safe financial modelling in OCaml.

Algebraic Effect — An OCaml 5 mechanism for structured side effects. Effects are declared, performed, and handled separately, enabling dependency injection, coroutines, and resumable computations without monads.

Dune — The standard OCaml build system. Uses declarative dune files to describe libraries, executables, and tests. Supports incremental builds, cross-compilation, and opam integration.

Functor (OCaml) — A module parameterised by another module. Enables generic algorithms that work over any type satisfying an interface. Not to be confused with the Haskell/category-theory functor.

GADT (Generalised Algebraic Data Type) — An ADT where the return type of each constructor can vary. Enables type-indexed computations where the type system encodes invariants (e.g., a typed expression tree).

Module — OCaml's unit of code organisation. Modules have signatures (interfaces) and structures (implementations). Modules can be nested, parameterised (functors), and passed as first-class values.

opam — The OCaml package manager. Manages compiler versions (switches), library dependencies, and build environments. The opam install command installs packages from the opam repository.

Phantom Type — A type parameter that appears in the type signature but not in the runtime representation. Used for zero-cost compile-time tagging (e.g., currency, lifecycle state, day count convention).

PPX (Preprocessor Extension) — A compile-time code transformation in OCaml. ppx_deriving generates boilerplate (show, compare, yojson) from type definitions. ppx_jane provides Jane Street's suite of derivers.

Property-Based Testing — A testing methodology where tests specify properties (invariants) that must hold for all inputs, and a framework (QCheck in OCaml) generates random inputs to find counterexamples.

QCheck — The standard OCaml property-based testing library. Provides generators, properties, and automatic shrinking of counterexamples. Integrates with Alcotest via QCheck_alcotest.

Tail Recursion — A recursive call where the recursive call is the last operation. OCaml optimises tail calls to avoid stack overflow. Essential for processing large financial datasets recursively.

Type Inference — OCaml's ability to deduce types without explicit annotations. The Hindley-Milner algorithm infers principal types. Reduces boilerplate while maintaining full static type safety.

Uniqueness Type / Mode — An OxCaml extension that tracks whether a value has a unique owner. Enables safe mutation and stack allocation without garbage collection overhead.

C.10 Machine Learning in Finance

Backtesting — The process of evaluating a trading strategy on historical data. Subject to overfitting, look-ahead bias, and survivorship bias. Walk-forward testing mitigates some of these issues.

Feature Engineering — The process of transforming raw market data into informative inputs for a model. Common features: returns, volatility, momentum, mean reversion signals, order book imbalance.

LSTM (Long Short-Term Memory) — A recurrent neural network architecture with gating mechanisms that allow it to learn long-range dependencies. Used for time series prediction in finance.

Overfitting — When a model learns the noise in training data rather than the underlying signal. Detected by poor out-of-sample performance. Regularisation (L1/L2), dropout, and cross-validation mitigate overfitting.

Reinforcement Learning (RL) — A machine learning paradigm where an agent learns to take actions to maximise cumulative reward. Applied to optimal execution, market making, and portfolio management.

Sharpe Ratio (as ML objective) — Often used as the objective function for financial ML models, as it directly measures risk-adjusted return rather than raw prediction accuracy.

Walk-Forward Optimisation — A backtesting methodology that repeatedly trains on a rolling window of historical data and tests on the subsequent out-of-sample period. More realistic than a single train/test split.

Terms are defined in context throughout the book. The chapter where each concept is introduced in depth is indicated in the text.