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We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of three coefficients: convexity, skew and kurtosis risk premium. We propose that option prices under the r…
We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark vulnerable claim there is an analytical solution, and we express it in terms of the Black-Scholes for…
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension regarding a general framework of interest rates in a fully collateralized market. It gives a new form…
Automated Market Makers based on concentrated liquidity, such as Uniswap v3, significantly improve capital efficiency but expose Liquidity Providers (LPs) to adverse selection costs, formalized as Loss-Versus-Rebalancing (LVR). While theoretical literature quantifies these costs, the interplay between realistic blockchain microstructure and endogenous pricing mechanisms remains under-explored. This paper develops a g…
The financial industry has undergone a significant transition from the London Interbank Offered Rates (LIBORs) to Risk Free Rates (RFRs) such as, e.g., the Secured Overnight Financing Rate (SOFR) in the U.S. and the Cash Rate (AONIA) in Australia, as primary benchmark rates for borrowing costs. The paper examines the pricing and hedging method for financial products in a cross-currency framework with the special emph…
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers the modeling of the liability liquidity risk (or funding liquidity), the second dimension is dedicated to the modeling of the asset liquidity risk (or market liquidity), whereas the third dimension considers the management of the asset-liability liquidi…
Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo) market. Recently, models were proposed to address this by computing a total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market.…
We investigate the optimal execution of contracts that are used in merger\&acquisition deals. We consider cash-settled and physically delivered contracts between a broker and a counterpart. Contracts are linear (total returns swaps), nonlinear (collar contracts) or Asian type (TWAP based contracts). We derive the optimal execution strategy and the optimal fee through indifference utility arguments allowing for linear…
Automated market makers (AMMs) for prediction markets descend from market scoring rules, where a mechanism operator subsidizes a market to aggregate beliefs about uncertain events. The existing literature has focused on bounding the total worst-case loss to the subsidizer, but has not addressed how that loss is distributed across price states or over time. We use the framework of loss-versus-rebalancing (LVR) to stud…
In the LIBOR era, banks routinely tied revolving credit facilities to credit-sensitive benchmarks. This study assesses the Across-the-Curve Credit Spread Index (AXI) -- a transparent, transaction-based measure of wholesale bank funding costs -- as a complement to SOFR, summarizing its behavior, construction, and loan-pricing implications. AXI aggregates observable unsecured funding transactions across short- and long…
We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, i.e., one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semi-linear BSDEs and PDEs, and thus it is necessary to solve the equations numerically. However, once it can be gua…
Financial decision systems require fast surrogate models for pricing, calibration, hedging, XVA, stress testing, and portfolio optimization. Standard neural surrogates reproduce prices or risk quantities, but downstream tasks depend as much on derivatives: deltas, vegas, curve and credit-spread sensitivities, exposure and objective gradients. We formulate a derivative-informed operator-learning framework in which the…
Retractions serve as an indicator of failures in research integrity, yet most analyses focus on absolute counts rather than risk per paper. We use one of the largest open bibliographic databases to develop incidence metrics normalized by population: retractions per publication and per active author annually. Applying an epidemiological framework that models counts with exposure, we find evidence of exponential growth…
Recent multimodal large language models have achieved strong performance in unified text and image understanding and generation, yet extending such native capability to 3D remains challenging due to limited data. Compared to abundant 2D imagery, high-quality 3D assets are scarce, making 3D synthesis under-constrained. Existing methods often rely on indirect pipelines that edit in 2D and lift results into 3D via optim…
Agent skills, structured packages of procedural knowledge and executable resources that agents dynamically load at inference time, have become a reliable mechanism for augmenting LLM agents. Yet inference-time skill augmentation is fundamentally limited: retrieval noise introduces irrelevant guidance, injected skill content imposes substantial token overhead, and the model never truly acquires the knowledge it merely…
We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advan…
Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We developed a hybrid hidden Markov framework that discretized excess growth rate…
VIX term structure tracks the shape of volatility futures across maturities and helps identify whether the market is pricing stable conditions or near-term stress.
Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.
Treasury auction tail measures how much the auction clears above or below the expected market yield, providing a sensitive signal of auction quality and investor demand.
US 10-Year Real Yield measures the inflation-adjusted yield on 10-year Treasuries and is a key benchmark for discount rates, financial conditions, and macro asset pricing.
US 10-Year Breakeven Inflation reflects the inflation rate implied by the gap between nominal Treasuries and TIPS, serving as a market-based gauge of long-term inflation expectations.
Funding stress signal derived from FX swap pricing distortions and balance sheet constraints.
Capacity Utilization — How tight industrial capacity is, informing pricing power and capex cycles.
Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.
Sovereign Default Risk — Probability and recovery pricing for government debt distress.
Black Scholes Model — Baseline European option pricing framework and Greek engine.
Binomial Tree Pricing — Discrete recombining tree for American and path-sensitive options.
Monte Carlo Option Pricing — Simulation pricing for path-dependent and multi-asset claims.
Dividend Risk Options — Call pricing sensitivity to unexpected dividend changes.
Fair Value Pricing (Systems).
Swing Pricing (Systems).
Gold Silver Ratio — Relative precious-metal pricing used in relative-value trades.
Spin Off Special Situation — Corporate separation creating forced flows and mispricings.
Unitranche Pricing 1M (Credit).
Unitranche Pricing 3M (Credit).
Unitranche Pricing 6M (Credit).
Unitranche Pricing 1Y (Credit).
Unitranche Pricing 2Y (Credit).
Unitranche Pricing 5Y (Credit).
Unitranche Pricing 7Y (Credit).
Unitranche Pricing 10Y (Credit).
Unitranche Pricing US IG (Credit).
Unitranche Pricing US HY (Credit).
Unitranche Pricing EU IG (Credit).
Unitranche Pricing EU HY (Credit).
Unitranche Pricing EM hard (Credit).
Unitranche Pricing financials (Credit).
Unitranche Pricing energy (Credit).
Unitranche Pricing autos (Credit).
Unitranche Pricing telecom (Credit).
Unitranche Pricing real estate (Credit).
Binomial Tree Pricing — Discrete recombining tree for American and path-sensitive options.
Black Scholes Model — Baseline European option pricing framework and Greek engine.
Capacity Utilization — How tight industrial capacity is, informing pricing power and capex cycles.
Funding stress signal derived from FX swap pricing distortions and balance sheet constraints.
Dividend Risk Options — Call pricing sensitivity to unexpected dividend changes.
Fair Value Pricing (Systems).
Gold Silver Ratio — Relative precious-metal pricing used in relative-value trades.
Monte Carlo Option Pricing — Simulation pricing for path-dependent and multi-asset claims.
Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.
Sovereign Default Risk — Probability and recovery pricing for government debt distress.
Spin Off Special Situation — Corporate separation creating forced flows and mispricings.
Swing Pricing (Systems).
Unitranche Pricing 10Y (Credit).
Unitranche Pricing 1M (Credit).
Unitranche Pricing 1Y (Credit).
Unitranche Pricing 2Y (Credit).
Unitranche Pricing 3M (Credit).
Unitranche Pricing 5Y (Credit).
Unitranche Pricing 6M (Credit).
Unitranche Pricing 7Y (Credit).
Unitranche Pricing autos (Credit).
Unitranche Pricing EM hard (Credit).
Unitranche Pricing energy (Credit).
Unitranche Pricing EU HY (Credit).
A funding-stress monitor can warn before equity volatility reprices.
A liquidity premium monitor can separate default risk from liquidity-driven spread widening.
Tracks policy reversal probability, market repricing windows, and timing mismatch between rhetoric and positioning.