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Fixed income has received far less attention than equity portfolio optimisation since Markowitz' original work of 1952, partly as a result of the need to model rates and credit risk. We argue that the shape of the efficient frontier is mainly controlled by linear constraints, with the standard deviation relatively unimportant, and propose a two-factor model for its time evolution.
We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai in 2003. The model by its nature can include fixed income securities as well in the portfolio. Under fairly general conditions, we prove the existence of optimal portfolio in both finite and infinite horizon problems.
In decentralized finance (DeFi), designing fixed-income lending automated market makers (AMMs) is extremely challenging due to time-related complexities. Moreover, existing protocols only support single-maturity lending. Building upon the BondMM protocol, this paper argues that its mathematical invariants are sufficiently elegant to be generalized to arbitrary maturities. This paper thus propose an improved design, B…
This paper explores several types of income which have not been explored so far by authors who tackled income and wealth distribution using Statistical Physics. The main types of income we plan to analyze are income before redistribution (or gross income), income of retired people (or pensions), and income of active people (mostly wages). The distributions used to analyze income distributions are Fermi-Dirac distribu…
Polynomial distribution can be applied to dynamical systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work to data regarding income from a more diversified pool of countries, which contains developed countries with high income, developed countries with middle income, developing and unde…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky se…
This dissertation reports work where physics methods are applied to financial and economical problems. The first part studies stock market data (chapter 1 to 5). The second part is devoted to personal income in the USA (chapter 6). We first study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. For mesoscopic times the bulk of the dis…
Automated market maker (AMM) fee rules are often evaluated by liquidity-provider (LP) welfare, but that objective mixes fee revenue, adverse-selection loss (loss-versus-rebalancing, LVR), routing response, and liquidity supply. Fixed-fee Uniswap v3 history cannot separate these channels or identify counterfactual trader-facing dynamic-fee rules. Real fee-related variation nonetheless exists: the Uniswap protocol-fee …
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form op…
This book, which is in Spanish, provides detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility (as an asset class), real estate, distressed assets, cash, cryptocurrencies, miscella…
We review the main changes in the interbank market after the financial crisis started in August 2007. In particular, we focus on the fixed income market and we analyse the most relevant empirical evidences regarding the divergence of the existing basis between interbank rates with different tenor, such as Libor and OIS. We also discuss a qualitative explanation of these effects based on the consideration of credit an…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review t…
We consider the problem of concurrent portfolio losses in two non-overlapping credit portfolios. In order to explore the full statistical dependence structure of such portfolio losses, we estimate their empirical pairwise copulas. Instead of a Gaussian dependence, we typically find a strong asymmetry in the copulas. Concurrent large portfolio losses are much more likely than small ones. Studying the dependences of th…
We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of $P(m)$. Precise solution…
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…
This paper compares different methods for forecasting the term structure of U.S. and European zero-coupon government bonds using both traditional econometric and Machine Learning (ML) approaches. We compare classical models (e.g., Dynamic Nelson-Siegel (DNS) and Principal Component Analysis (PCA)) with different Neural Network (NN) architectures, including those inspired by the classical models, on the U.S. Treasury …
We explore the interplay between sovereign debt default/renegotiation and environmental factors (e.g., pollution from land use, natural resource exploitation). Pollution contributes to the likelihood of natural disasters and influences economic growth rates. The country can default on its debt at any time while also deciding whether to invest in pollution abatement. The framework provides insights into the credit spr…
We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the order flow $N$ is given by a Poisson process, we give a full analysis of the properties and computation of the optimal dynamic execution strategy. Extensions, whereby (a) $N$ is a f…
Indirect bidder allotment tracks the share of Treasury auctions awarded to indirect bidders, often used as a proxy for foreign and institutional demand.
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.
Treasury auction bid-to-cover ratio measures the amount of demand relative to supply at an auction and is used to assess investor appetite for government debt.
Duration Risk — Interest-rate sensitivity of bond portfolios, amplified in low-yield high-duration regimes.
Convexity Risk — Non-linear price response to yield changes, especially relevant in MBS and long bonds.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
Steepener Flattener Trade — Curve trades expressing views on growth, inflation, and term premium independently of level.
Carry and Roll Down — Expected return from holding higher-yielding tenor as it rolls down a positively sloped curve.
Asset Swap Spread — Spread between bond yield and floating leg, linking credit and funding markets.
Z Spread — Static spread over the government curve capturing credit and liquidity premium.
Option-Adjusted Spread — Spread adjusted for embedded prepayment options in callable bonds and MBS.
MBS Prepayment Speed — Refinancing and turnover driven cash-flow uncertainty in agency mortgages.
TBA Roll Specialness — Delivery-option value in TBA markets signaling collateral scarcity or abundance.
Agency MBS Basis — Spread between MBS and hedging Treasury futures, a core RV monitor.
Commercial Mortgage Delinquency — Office and retail stress feeding through CRE credit and regional bank risk.
Leveraged Loan Index — Floating-rate corporate credit sensitive to defaults, spreads, and CLO demand.
CLO Issuance — Structured credit supply that absorbs leveraged loans and shapes spread regimes.
Distressed Debt Ratio — Share of debt trading at deep discounts — early warning for credit cycle turns.
Fallen Angels — Investment-grade downgrades into high yield, creating forced selling and index rebalancing flows.
Rising Stars — High-yield upgrades into investment grade, often supporting spread tightening episodes.
CDS Basis Trade — Arbitrage between cash bonds and CDS contracts revealing funding and counterparty frictions.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
Primary Dealer Survey — Desk-level policy expectations that front-run official communications.
Iron Condor Structure — Short vol range trade expressing view of subdued movement between strikes.
Covered Call (Derivatives).
CMBS Delinquency (Fixed Income).
CLO Spreads (Fixed Income).
Leveraged Loan Price (Fixed Income).
HY OAS (Fixed Income).
IG OAS (Fixed Income).
Fallen Angel Risk (Fixed Income).
Rising Star Credit (Fixed Income).
Default Rate Cycle (Fixed Income).
Recovery Rate Cycle (Fixed Income).
Distressed Ratio (Fixed Income).
Catastrophe Bond (Fixed Income).
5y5y Forward Inflation (Fixed Income).
ABS Tranche 10Y (Fixed Income).
ABS Tranche 1M (Fixed Income).
ABS Tranche 1Y (Fixed Income).
ABS Tranche 20Y (Fixed Income).
ABS Tranche 2Y (Fixed Income).
ABS Tranche 30Y (Fixed Income).
ABS Tranche 3M (Fixed Income).
ABS Tranche 5Y (Fixed Income).
ABS Tranche 6M (Fixed Income).
ABS Tranche 7Y (Fixed Income).
ABS Tranche agency (Fixed Income).
ABS Tranche Australia (Fixed Income).
ABS Tranche belly (Fixed Income).
ABS Tranche Canada (Fixed Income).
ABS Tranche CEEMEA (Fixed Income).
ABS Tranche China (Fixed Income).
ABS Tranche EM Asia (Fixed Income).
ABS Tranche Euro Area (Fixed Income).
ABS Tranche front (Fixed Income).
ABS Tranche HY (Fixed Income).
ABS Tranche IG (Fixed Income).
ABS Tranche Japan (Fixed Income).
ABS Tranche LatAm (Fixed Income).