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We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to con…
We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments, and featuring collateralization in any currency denominations. In view of this, we first provide a thorough study of cross-currency markets in the presence of collateral and incompleteness. Then we give a general treatment of collateral dislocations by describing the instantaneous…
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…
We study a speculative trading problem within the exploratory reinforcement learning (RL) framework of Wang et al. [2020]. The problem is formulated as a sequential optimal stopping problem over entry and exit times under general utility function and price process. We first consider a relaxed version of the problem in which the stopping times are modeled by the jump times of Cox processes driven by bounded, non-rando…
This paper develops an autonomous framework for systematic factor investing via agentic AI. Rather than relying on sequential manual prompts, our approach operationalizes the model as a self-directed engine that endogenously formulates interpretable trading signals. To mitigate data snooping biases, this closed-loop system imposes strict empirical discipline through out-of-sample validation and economic rationale req…
In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one of the main goals being also that of exhibiting an "adjustment factor" when passing from the one-cu…
In this paper, we compare static and dynamic (reduced form) approaches for modeling wrong-way risk in the context of CVA. Although all these approaches potentially suffer from arbitrage problems, they are popular (respectively) in industry and academia, mainly due to analytical tractability reasons. We complete the stochastic intensity models with another dynamic approach, consisting in the straight modeling of the s…
We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations…
In this paper, we develop a novel method based on Malliavin calculus to find an approximation for the convexity adjustment for various classical interest rate products. Malliavin calculus provides a simple way to get a template for the convexity adjustment. We find the approximation for Futures, OIS Futures, FRAs, and CMSs under a general family of the one-factor Cheyette model. We have also seen the excellent qualit…
This paper provides intuition on the relationship of accrual and mark-to-market valuation for cash and forward interest rate trades. Discounted cashflow valuation is compared to spread-based valuation for forward trades, which explains the trader's view on valuation. This is followed by Taylor series approximation for cash trades, uncovering simple intuition behind accrual valuation and mark-to-market adjustment. It …
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIBOR model and aim at developing accurate and efficient log-Lévy approximations for the dynamics of th…
The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe the market of interest rate products. On the other hand, using different yield curves at the same time requires a reformulation of most of the basic assumptions made in interest ra…
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…
Persistent shifts in term-structure dynamics undermine the stability of single-regime models in long samples. We develop an arbitrage-free regime-switching generalized CIR (RS-GCIR) model that jointly prices the Chinese government bond (CGB) curve and corporate bond curves. To capture the systematic transmission from interest-rate conditions to credit spreads, we structure the model into two blocks and price corporat…
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…
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 liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers the asset-liability management of the liquidity gap risk (or asset-liability…
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 liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers asset-liability liquidity risk management (or asset-liability matching). The…
BTP-Bund spread measures the yield difference between Italian and German government bonds and is a key indicator of euro-area sovereign stress and fragmentation risk.
Equity Risk Premium measures the excess return investors expect from equities over risk-free assets and is a core framework for evaluating relative equity valuation.
FRA-OIS spread measures the difference between interbank funding expectations and overnight indexed swap rates, often used as a gauge of banking and short-term funding stress.
GARCH Volatility Model — Conditional heteroskedasticity framework for forecasting volatility clusters.
Kelly Criterion — Optimal growth bet sizing framework — fragile with estimation error.
Regime Switching Model — Statistical frameworks where parameters shift between discrete market states.
Europe Periphery Spreads — BTP-Bund and similar spreads as euro-area fragmentation gauges.
Stress Testing Framework — Scenario PnL under historical and hypothetical shock libraries.
Black Scholes Model — Baseline European option pricing framework and Greek engine.
FRA Rate (Rates).
Fractional Differentiation (Systems).
Mean Variance Optimization — Classic Markowitz optimization — fragile to inputs.
Common Framework Debt (Emerging Markets).
Lit Market Fragmentation — Split liquidity across exchanges raising routing complexity.
Forward Rate Agreement (Rates).
Multi Curve Framework — Separate projection and discount curves after the crisis.
Market Impact Model Almgren — Temporary and permanent impact framework for optimal execution.
Swiss Franc Safe Haven (FX).
Lit Fragmentation US equities — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation EU equities — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation futures — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation ETF — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation options — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation FX spot — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation Treasury — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation IG credit — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation HY credit — Execution quality, book dynamics, or venue microstructure concept.
Lit Fragmentation crypto — Execution quality, book dynamics, or venue microstructure concept.
FRA Strip 1M (Rates).
FRA Strip 3M (Rates).
FRA Strip 6M (Rates).
FRA Strip 1Y (Rates).
FRA Strip 2Y (Rates).
FRA Strip 5Y (Rates).
FRA Strip 7Y (Rates).
FRA Strip 10Y (Rates).
Black Scholes Model — Baseline European option pricing framework and Greek engine.
BTP-Bund spread measures the yield difference between Italian and German government bonds and is a key indicator of euro-area sovereign stress and fragmentation risk.
Common Framework Debt (Emerging Markets).
Equity Risk Premium measures the excess return investors expect from equities over risk-free assets and is a core framework for evaluating relative equity valuation.
Europe Periphery Spreads — BTP-Bund and similar spreads as euro-area fragmentation gauges.
Flash Crash Fragility Australia (Liquidity).
Flash Crash Fragility Canada (Liquidity).
Flash Crash Fragility carry (Liquidity).
Flash Crash Fragility CEEMEA (Liquidity).
Flash Crash Fragility China (Liquidity).
Flash Crash Fragility disinflation (Liquidity).
Flash Crash Fragility easing (Liquidity).
Flash Crash Fragility EM Asia (Liquidity).
Flash Crash Fragility Euro Area (Liquidity).
Flash Crash Fragility Japan (Liquidity).
Flash Crash Fragility LatAm (Liquidity).
Flash Crash Fragility liquidity-crisis (Liquidity).
Flash Crash Fragility month-end (Liquidity).
Flash Crash Fragility quarter-end (Liquidity).
Flash Crash Fragility recession (Liquidity).
Flash Crash Fragility reflation (Liquidity).
Flash Crash Fragility risk-off (Liquidity).
Flash Crash Fragility risk-on (Liquidity).
Flash Crash Fragility stagflation (Liquidity).