Papers, wiki, Option Blackboard, encyclopedia, and cards.
Credit Value Adjustment (CVA) is the difference between the value of the default-free and credit-risky derivative portfolio, which can be regarded as the cost of the credit hedge. Default probabilities are therefore needed, as input parameters to the valuation. When liquid CDS are available, then implied probabilities of default can be derived and used. However, in small markets, like the Nordic region of Europe, the…
ESG ratings provide a quantitative measure for socially responsible investment. We present a unified framework for incorporating numeric ESG ratings into dynamic pricing theory. Specifically, we introduce an ESG-valued return that is a linearly constrained transformation of financial return and ESG score. This leads to a more complex portfolio optimization problem in a space governed by reward, risk and ESG score. Th…
Risk management is a prominent issue in peer-to-peer lending. An investor may naturally reduce his risk exposure by diversifying instead of putting all his money on one loan. In that case, an investor may want to minimize the Value-at-Risk (VaR) or Conditional Value-at-Risk (CVaR) of his loan portfolio. We propose a low degree of freedom deep neural network model, DeNN, as well as a high degree of freedom model, DSNN…
Neural and numerical policy solvers can produce feasible controls even when the optimal rule and its binding constraints are unavailable. A primal-dual bracket certifies value loss, but it does not locate the optimal policy or explain which constraints genuinely bind. We show that, on the same declared simulation grid, one bracket can support both conclusions. For polyhedral controls, an exact conditional budget iden…
This article studies a dynamic corporate risk management problem by considering the decision-making of risk-averse managers who exert costly effort and select project risk. We study how a Value-at-Risk (VaR) constraint affects managerial decisions and the distribution of firm value when the manager's objective is non-concave with a fixed salary and options. By the concavification technique, we analyze the optimal ter…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value analysis for infinite correlated systems remains an open challenge, we propose a practical framework for handling a large but finite number of correlated time series. We develop our …
Corporate insiders trade for diverse reasons, often possessing Material Non-Public Information (MNPI). Determining whether specific trades leverage MNPI is a significant challenge due to inherent complexity. This study focuses on two critical objectives: accurately detecting Unlawful Insider Trading (UIT) and identifying key features explaining classification. The analysis demonstrates how combining Shapley Values (S…
We revisit Gerber's Informational Quality (IQ) framework, a data-driven approach for constructing correlation matrices from co-movement evidence, and address two obstacles that limit its use in portfolio optimization: guaranteeing positive semidefinite ness (PSD) and controlling spectral conditioning. We introduce a squeezing identity that represents IQ estimators as a convex-like combination of structured channel ma…
A model is developed to assess the profitability of loans or mortgages with a specified repayment schedule. Financial institutions face two competing risks: default and prepayment, both influenced by the stochastic evolution of credit market conditions. This study focuses on the Random Net Present Value (RNPV) as a key performance metric. The analysis evaluates the mean and variance of the RNPV at both the individual…
We consider the investor who doesn't trade shares of his portfolio. The investor only observes the current trades made in the market with his securities to estimate the current return, variance, and risks of his unchanged portfolio. We show how the time series of consecutive trades made in the market with the securities of the portfolio can determine the time series that model the trades with the portfolio as with a …
This paper provides a comprehensive empirical analysis of the economics and dynamics behind arbitrages between centralized and decentralized exchanges (CEX-DEX) on Ethereum. We refine heuristics to identify arbitrage transactions from on-chain data and introduce a robust empirical framework to estimate arbitrage revenue without knowing traders' actual behaviors on CEX. Leveraging an extensive dataset spanning 19 mont…
This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool's value using a combination of European calls and puts. Furthermore, we establish a result guaranteeing hedging coverage for all final prices within a predefined interval. These theoretical results motivate a numerical…
We study a stochastic control problem with regime switching arising in an optimal liquidation problem with dark pools and multiple regimes. The new feature of this model is that it introduces a system of BSDEs with jumps and with singular terminal values, which appears in literature for the first time. The existence result for this system is obtained. As a result, we solve the stochastic control problem with regime s…
Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified horizon (such as one day or ten days) at a desired confidence level (such as 95'th percentile). In scenario design and stress testing, the goal is to construct extreme market scenario…
Since 2016 the operation of insurance companies in the European Union is regulated by the Solvency II directive. According to the EU directive the capital requirement should be calculated as a 99.5\% of Value at Risk. In this study, we examine the impact of this capital requirement constraint on equilibrium premiums and capitals. We discuss the case of the oligopoly insurance market using Bertrand's model, assuming p…
A highly relevant problem of modern finance is the design of Value-at-Risk (VaR) optimal portfolios. Due to contemporary financial regulations, banks and other financial institutions are tied to use the risk measure to control their credit, market, and operational risks. Despite its practical relevance, the non-convexity induced by VaR constraints in portfolio optimization problems remains a major challenge. To addre…
Previous work suggests that the charter value hypothesis is theoretically grounded and empirically supported, but not universally. Accordingly, this paper aims to perform an analysis of the relations between charter value, risk taking, and supervision, taking into account the relations' complexity. Specifically, using the CAMELS rating system as a general framework for supervision, we study how charter value relates …
This study introduces an advanced machine learning method for predicting soccer players' market values, combining ensemble models and the Shapley Additive Explanations (SHAP) for interpretability. Utilizing data from about 12,000 players from Sofifa, the Boruta algorithm streamlined feature selection. The Gradient Boosting Decision Tree (GBDT) model excelled in predictive accuracy, with an R-squared of 0.901 and a Ro…
Attention builds a weighted average of values, with weights from a compatibility function of queries and keys. It lets a model focus on relevant parts of a context instead of a single fixed vector.
Policy gradient methods optimize a parameterized policy π_θ directly by ascending the gradient of expected return, rather than via an action-value table.
Q-learning is an off-policy TD method that learns action values Q(s, a) toward the greedy target r + γ max_a′ Q(s′, a′), without needing the behavior policy to be optimal.
Self-attention is attention where queries, keys, and values all come from the same sequence, so each position can mix information from every other position in one layer.
Credit Valuation Adjustment — Adjustment to derivative value for counterparty default risk.
Market-neutral futures spreads — calendar, inter-commodity, or intra-curve — a CTA that tries not to own outright direction.
Long one commodity, short a related one — WTI/Brent, gold/silver, corn/wheat, gas/power — a relative-value family across complexes.
A multi-premia CTA that runs trend and carry (and sometimes value) as separately budgeted families — the modern large-platform stack.
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
Moneyness is where spot sits versus strike — in, at, or out of the money — the first map of option value and of Greek shape.
Notional value is the face amount a derivative references — the exposure scale, not the cash outlay or the market value.
Greeks are the sensitivities of option value to spot, vol, time, and rates — the risk report of a non-linear book.
Theta is the sensitivity of option value to the passing of time — the daily rent of holding convexity.
Vega is the sensitivity of option value to implied volatility — the vol-dollar you are long or short.
Catching a falling knife is buying a crashing asset because it ‘looks cheap,’ without a catalyst or a hedge — you can catch it, but you usually bleed.
Cheap and rich are relative-value words: cheap means wide or low versus a model, a history, or a hedge; rich means tight or expensive on that same yardstick — not ‘I like the story.’
CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.
DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.
Gresham’s law is that bad money drives out good when both are legal tender at a fixed rate: the overvalued coin circulates, the undervalued one is hoarded or exported.
Opportunity cost is the value of the next-best alternative you give up when you choose one use of a scarce resource — time, capital, balance-sheet, or a risk limit.
Ricardian equivalence says deficit-financed tax cuts do not raise demand if agents save the transfer to pay the future tax — debt and taxes are two labels on the same present-value burden.
Seigniorage is the real resources a sovereign (or a private issuer of money-like claims) obtains by issuing money whose production cost is below face value.
GDP is the market value of final goods and services produced in an economy over a period — the size of the flow, not the wealth stock.
Book value is accounting equity — assets minus liabilities on the books, not what a willing buyer would pay tonight.
Diluted shares are the share count as if in-the-money options, convertibles, and other claims were exercised — the honest denominator for EPS and value.
Enterprise value is the market value of operating assets — equity plus net debt and other non-equity claims, minus non-operating cash.
Market capitalization is share price times diluted shares — the market value of residual equity, not the value of the firm.
NAV is the fund’s assets minus liabilities, per share — the accounting price at which open-end vehicles deal.
A poison pill is a rights plan that dilutes a bidder who crosses an ownership trigger — a delay and bargaining chip, not a value creation.
Price-to-book is market cap divided by book equity — what the market pays per unit of accounting residual.
Shareholders' equity is residual interest in assets after deducting liabilities — book capital, not the market cap.
A stock split increases shares outstanding and cuts the price by the same factor — cosmetics on the claim, not on enterprise value.
A value stock screens cheap on book, earnings, or cash flow — a low multiple that can be a bargain or a melting ice cube.
Argentina’s 2001–02 collapse ended the convertibility 1:1 peg with default, corralito, and a violent real devaluation — a political-economy crisis of an overvalued peg.
Credit Suisse’s March 2023 state-brokered sale to UBS wrote AT1s to zero while common equity kept residual value — a hierarchy shock that repriced the entire AT1 market.
Russia’s August 1998 default and devaluation blew up leveraged relative-value books, culminating in the LTCM rescue — a reminder that ‘hedged’ can mean ‘short liquidity in every state.’
Argentina’s 2001–02 collapse ended the convertibility 1:1 peg with default, corralito, and a violent real devaluation — a political-economy crisis of an overvalued peg.
Attention builds a weighted average of values, with weights from a compatibility function of queries and keys. It lets a model focus on relevant parts of a context instead of a single fixed vector.
Book value is accounting equity — assets minus liabilities on the books, not what a willing buyer would pay tonight.
Cheap and rich are relative-value words: cheap means wide or low versus a model, a history, or a hedge; rich means tight or expensive on that same yardstick — not ‘I like the story.’
Trade refined-product minus crude (crack) or nearby-versus-deferred calendars — commodity relative value, not a directional oil call.
Credit Suisse’s March 2023 state-brokered sale to UBS wrote AT1s to zero while common equity kept residual value — a hierarchy shock that repriced the entire AT1 market.
Credit Valuation Adjustment — Adjustment to derivative value for counterparty default risk.
CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.
Market-neutral futures spreads — calendar, inter-commodity, or intra-curve — a CTA that tries not to own outright direction.
Long undervalued currencies and short overvalued ones versus purchasing-power parity or real-rate gaps — FX value, slow and mean-reverting.
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
Diluted shares are the share count as if in-the-money options, convertibles, and other claims were exercised — the honest denominator for EPS and value.
DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.
An eigenvalue λ of A satisfies A v = λ v. In risk, eigenvalues of the covariance matrix are the variances of the principal components — they tell you how many true factors you have.
Enterprise value is the market value of operating assets — equity plus net debt and other non-equity claims, minus non-operating cash.
Expected value is the probability-weighted average of a random variable — the center of the distribution you actually face, not the mode or the ‘base case’ slide.
The three-factor model adds size (SMB) and value (HML) to the market — a better cross-section than CAPM, still not the last word.
Gresham’s law is that bad money drives out good when both are legal tender at a fixed rate: the overvalued coin circulates, the undervalued one is hoarded or exported.
GDP is the market value of final goods and services produced in an economy over a period — the size of the flow, not the wealth stock.
Long one commodity, short a related one — WTI/Brent, gold/silver, corn/wheat, gas/power — a relative-value family across complexes.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
The law of large numbers says the sample average converges to the expected value as n grows — the reason insurance and a large independent bet-set work, and a small correlated book does not.
Macaulay duration is the present-value-weighted average time to receive a bond’s cash flows — duration in years, before the modified-duration hedge ratio.
Rank on earnings yield and return on capital, buy the top combined rank — Greenblatt’s two-factor quality-value screen.