Technical Glossary

• Stochastic Stochastic can be simply understood as “random” or acting according to a random probability distribution In finance, stochastic models are used to represent the seemingly random behavior of financial markets, helping to calculate derivative prices, value at risk, etc. Examples of such models include the Black-Scholes-Merton model for options pricing or various kinds of stochastic volatility models.

• Volatility In finance, volatility refers to the degree of variation in a financial instrument's price over time. It is often measured as the standard deviation of the asset's returns. High volatility indicates that the price of the asset can change dramatically over a short period in either direction, representing higher uncertainty or risk. Conversely, low volatility indicates that an asset's value does not fluctuate dramatically, implying lower risk.

  • Implied volatility (IV) The expected volatility of a stock or other asset, as predicted by the market price of options or derivatives.

  • Standard deviation A statistical measure that captures the dispersion or variability in a set of data points. In finance, it's commonly used to gauge the volatility or risk associated with a particular investment. A higher standard deviation indicates a wider range of potential outcomes and therefore greater uncertainty or risk.

• Black-Scholes-Merton (BSM) models A formula to calculate the fair price of an option. It uses factors like the stock price, strike price, volatility, time, and risk-free rate. It is also used to help manage internal risk via the Greeks.

  • The Greeks The "Greeks" in finance are a set of statistical values that provide a way to measure the sensitivity of an option's value to various factors. The key Greeks are delta, gamma, vega, theta, and rho.

    • Delta Delta is the rate at which the price of an option changes for each unit change in the price of the underlying asset. It's a measure of an option's sensitivity.

    • Rho Rho: This measures the sensitivity of an option's price to changes in the interest rate. It represents the expected change in an option's price for a 1% change in interest rates.

    • Vega Measures how much an option's price changes given a 1% change in implied volatility of the underlying asset.

    • Gamma Reflects the rate of change in an option's Delta for a $1 change in the price of the underlying asset.

    • Theta Represents the rate of decrease in the price of an option due to the passage of time, also known as time decay.

  • Delta-gamma hedging Delta-gamma hedging is a strategy which reduces the risk of price movements in an underlying asset by offsetting delta (price risk) and gamma (rate of change in delta) risk by holding positions in the underlying asset and its derivatives (usually options).

  • Vega hedging Vega hedging is a strategy to minimize the effect of a change in an assets implied volatility by taking a position that has an opposite vega to the initial position.

• Root-finding techniques Algorithms which find roots of a given function, i.e., the values at which the function equals zero, when the function does not (usually) have a closed form solution. Examples include the bisection method, Newton's method, and the secant method. Concrete uses them to determine the implied volatility calculated by outside firms.

• Ruin theory Also known as the theory of solvency, it is a branch of mathematical finance and actuarial science that studies the risk of an insurance company or financial institution becoming insolvent. The theory models the company's capital over time as a stochastic process and computes the probability of ruin, i.e., the probability that the company's capital falls below zero. It also investigates the distribution of the surplus immediately before ruin and the deficit at ruin.

  • Cramer-Lundberg model Primary ruin theory model used to manage insurance company's ruin probability. It assumes that claims occur according to a Poisson process and that claim amounts are independent and identically distributed. The ruin probability is calculated over an infinite time horizon by considering the interplay of income from premiums and losses from claims.

• Value-at-risk (VaR) models A statistical technique used to measure and quantify the level of financial risk within a firm, portfolio, or position over a specific time frame. It provides an estimate of the maximum loss that can be expected with a certain level of confidence, for instance, a 5% VaR of $1 million over a 1-day period suggests a 5% chance of losing $1 million or more in a day.

  • Conditional value-at-risk Estimates worst-case losses under extreme conditions, beyond the Value-at-Risk. It's the average loss in the worst scenarios.

• Extreme value theory A branch of statistics dealing with the extreme deviations from the median of probability distributions. In finance, EVT is used to measure and quantify the risk of extreme market events, such as significant declines in asset prices or market crashes. This theory assists in predicting the magnitude of the most significant potential losses over a given time period.

  • Peak over threshold (PoT) method A statistical technique used in Extreme Value Theory for estimating the probability of extreme events. This method involves setting a threshold, and focusing on the values that exceed this threshold. It's often used in fields like finance, meteorology, and engineering to predict the likelihood and impact of rare and extreme events.

• Jump diffusion A model capturing sudden, large changes ("jumps") in asset prices, beyond regular fluctuations. Used by Concrete’s pricing engine in concert via a modified Black-Scholes-Merton model.

• Machine learning (ML) models Algorithms that allow computers to learn from data and make predictions or decisions without being explicitly programmed. Examples include linear regression, decision trees, support vector machines, and neural networks. They're used for tasks like predicting future trends, classification, and anomaly detection.

  • Long short term memory (LSTM) model A type of recurrent neural network (RNN) architecture used in the field of deep learning. Unlike standard feedforward neural networks, LSTM has feedback connections and can process entire sequences of data, making it well-suited for time series prediction tasks.

  • Gradient boosted decision tree (GBDT) A machine learning technique that constructs new models to predict residuals or errors of prior models and then adds them together to make the final prediction. It combines weak learning models to form a robust predictive model, reducing bias and variance.

  • Convolutional Neural Networks (CNNs) A class of deep neural networks primarily employed in the processing of grid-like data structures such as images. Unlike fully connected networks, CNNs utilize convolutional layers that apply convolutional filters to local input features, enabling hierarchical feature extraction and reducing the number of parameters, thereby making them adept for tasks like image recognition.

• Asymmetric volatility model Overarching volatility model class that accounts for the leverage effect. To be specific, the leverage effect describes the phenomena that negative returns (price decreases) create greater subsequent volatility than positive returns of the same magnitude. Examples of such models include the AS-GARCH model and the CS-GARCH model, which allow for different reactions in volatility to positive and negative price changes.

• Generalized auto-regressive integrate heteroscedasticity (GARCH) model A statistical model that describes time-varying volatility in financial data. It captures the tendency for large changes in financial returns to be followed by further large changes and for small changes to be followed by small changes.

  • Asymmetric power GARCH (AS-GARCH) model Type of Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model that allows for asymmetry in the response of volatility to positive and negative shocks, and where the variance dynamics can be non-linear. This captures the 'leverage effect', where negative shocks tend to have a greater impact on volatility than positive shocks of the same magnitude. The 'power' aspect allows for further flexibility in how the conditional variance responds to shocks.

  • Component standard GARCH (CS-GARCH) model This is an extension of the traditional GARCH model that includes multiple components to capture different aspects of volatility. Typically, this includes a short-run or transitory component and a long-run or persistent component. This allows the model to capture more complex patterns in volatility, such as sudden shocks and slower, longer-lasting changes. The model provides a more nuanced understanding of how volatility behaves over time.

• Uncertain volatility models (UVMs) Overarching class of volatility model in which implied volatility is modeled as being within a certain range. UVMs are well-suited to determining optimal super-hedging and sub-hedging strategies under the assumption that the volatility lies between two bounds. These bounds are stochastically defined.

• Multi-criteria decision-making (MCDM) model A class of decision-making models that apply mathematical methods and algorithms to evaluate, rank, and select alternatives based on several criteria. This methodology is designed to assist in scenarios where decisions involve multiple conflicting objectives.

• Auto-regressive integrated moving average (ARIMA) model A forecasting technique that projects future values of a series based on its own past values, its past error terms, and a moving average model. It's a popular model for analyzing and forecasting time series data in fields like economics and finance.

  • Auto-regressive fractionally integrated moving average (ARFIMA) model This model is an extension of the ARIMA model, designed to handle time series data with long memory properties. This means that even small shocks can have a long-lasting impact, which decay slowly over time. The fractionally differencing parameter allows for greater flexibility in modeling this long-term dependence.

• Semi-soul bound token (SSBT) SSBTs are specific kind of ERC-721 that do not allow for the transfer of the token away from the original holding wallet.

• ERC 721 ERC 721 token is a unique token that represent an asset that is distinct from the identity of the underlying asset. That is to say, ERC-721s correspond to, and represent, a specific/unique asset. Concrete uses them to represent loans and policies

• Vault A vault is a smart contract that allows users to deposit their cryptocurrency into a single pool. Most vaults are used for automated investment strategies including lending, borrowing, liquidity provision, etc. Concrete vaults are used as capital to cover policies in the event they claim due to liquidation. To be specific, the collateral used to prevent liquidations is here.

• Derivatives Financial contracts whose value depends on the performance of an underlying asset, index, or interest rate. They're used for hedging risks, speculating on future price movements, and gaining access to otherwise hard-to-trade assets or markets.

  • Options Financial instruments that give the holder the right, but not the obligation, to buy (call option) or sell (put option) an underlying asset at a predetermined price before or on a specific future date.

  • Put Spread A type of options strategy that involves buying and selling two put options simultaneously. The investor buys a put option at a specific strike price and sells another put option at a lower strike price, aiming to profit from a modest decrease in the underlying asset's price. Concrete’s coverage policies are well-modeled by put spreads.

• Perpetuals Perpetuals are a type of derivative contract that doesn't have an expiry date, unlike traditional futures contracts. This means they can be held indefinitely. They're commonly used in cryptocurrency markets, allowing traders to speculate on the future price of the underlying asset without ever needing to own the asset itself. The price of perpetual futures tends to stay close to the spot price of the underlying asset through a mechanism called a funding rate.

• Funding rate Funding rates are a mechanism to ensure the price of the perpetual contract stays 'anchored' to the underlying asset's spot price and maintain equilibrium. When the perpetual contract trades at a premium compared to the spot price (indicating more longs), the funding rate is positive, and long traders pay shorts. Conversely, if the contract trades at a discount (indicating more shorts), the funding rate is negative, and short traders pay longs.

• Loan-to-value ratio A financial metric used by lenders to express the ratio of a loan to the value of an asset purchased. Higher LTV ratios are higher risk. LTV threshold are used by lenders like AAVE to determine liquidations and by Concrete to determine collateral deposits etc.

• Linear model A statistical model where the relationship between the dependent variable and the independent variables is assumed to be linear. This means that a change in any independent variable will result in a consistent change in the dependent variable, regardless of the values of the other independent variables. Common examples of linear models include simple linear regression and multiple linear regression. These models are widely used in finance for forecasting and trend analysis.

• Factor model Type of linear model that decomposes a time series variable into a limited number of unobservable underlying factors. The factors typically represent systematic, non-diversifiable influences that affect multiple assets simultaneously. Concrete’s factor model used in the collateral risk engine uses factors such as trading volume, sentiment, and interest rates.

• Simulation engine A computational tool used to simulate various types of market behavior. They can generate possible future paths for various financial variables such as stock prices, interest rates, and volatilities, using techniques such as Monte Carlo simulation or stochastic process simulation. Concrete’s simulation engine is vital in ensuring resilience in the face of black swan events.