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Central banks manage about \$12 trillion in foreign exchange reserves, influencing global exchange rates and asset prices. However, some of the largest holders of reserves report minimal information about their currency composition, hindering empirical analysis. I describe a Hidden Markov Model to estimate the composition of a central bank's reserves by relating the fluctuation in the portfolio's valuation to the exc…
After the release of the final accounting standards for impairment in July 2014 by the IASB, banks will face the next significant methodological challenge after Basel 2. In this paper, first methodological thoughts are presented, and ways how to approach underlying questions are proposed. It starts with a detailed discussion of the structural conservatism in the final standard. The exposure value iACV(c) (idealized A…
This study examines active liquidity management by Indian open-ended equity mutual funds. We find that fund managers respond to inflows by increasing cash holdings, which are later used to purchase less-liquid stocks at favourable valuations. Funds with less liquid portfolios tend to maintain larger cash reserves to manage flows. Funds that make active liquidity choices yield statistically and economically significan…
We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader-follower stochastic game, where the venue is the leader and a representative LP is the follower. We derive approximate closed-form equilibrium solutions to the stochastic game and analyze the …
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted) geometric mean. This paper extends several results known for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights. These results inc…
Current post-trade clearing systems rely almost exclusively on cash or cash-like collateral, leaving vast reserves of short-term liquidity embedded in trade credit outside formal settlement infrastructures. A key barrier to integrating this liquidity is the near-universal dependence of clearing services on novation, which imposes institutional overhead that restricts accessibility and limits the range of obligations …
A physically backed leveraged event position requires real credit: if collateral C receives leverage L, the protocol supplies (L-1)C and uses the combined amount to acquire recognized event exposure. This paper develops a venue-agnostic on-chain credit architecture for that capital layer and an endogenous model of its capital market. It separates traders, Senior Credit LPs, market makers, liquidators, and Liquidation…
Deep reinforcement learning (DRL) has been envisioned to have a competitive edge in quantitative finance. However, there is a steep development curve for quantitative traders to obtain an agent that automatically positions to win in the market, namely \textit{to decide where to trade, at what price} and \textit{what quantity}, due to the error-prone programming and arduous debugging. In this paper, we present the fir…
Automated market makers (AMM) have grown to obtain significant market share within the cryptocurrency ecosystem, resulting in a proliferation of new products pursuing exotic strategies for horizontal differentiation. Yet, their theoretical properties are curiously homogeneous when a set of basic assumptions are met. In this paper, we start by presenting a universal approach to deriving a formula for liquidity provisi…
As deep reinforcement learning (DRL) has been recognized as an effective approach in quantitative finance, getting hands-on experiences is attractive to beginners. However, to train a practical DRL trading agent that decides where to trade, at what price, and what quantity involves error-prone and arduous development and debugging. In this paper, we introduce a DRL library FinRL that facilitates beginners to expose t…
Let $L=(L_s)_{0\le s\le t}$ be a cumulative net-loss process and let $M_t=\sup_{0\le s\le t}L_s$. For a candidate reserve $u$ and a distortion function $g$, define $D_g^{(t)}(u)=\int_u^\infty g(P(M_t>v))d v$. This function measures the tail-weighted residual severity of the largest cumulative loss over the horizon. We derive three monetary risk measures: its value at zero reserve and two measures based on fixed and p…
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that …
Concentrated-liquidity automated market makers (CLAMMs), as exemplified by Uniswap v3, are now a common primitive in decentralized finance frameworks. Their design combines continuous trading on constant-function curves with discrete tick boundaries at which liquidity positions change and rounding effects accumulate. While there is a body of economic and game-theoretic analysis of CLAMMs, there is negligible work tha…
Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision of liquidity at each tick under a given set of parameter estimates for swap volume and price volatility. Surprisingly, early results show that concentrating liquidity around the c…
We study the formation of an optimal interbank network in a model where banks control both their supply of liquidity, through cash reserves, and their exposures to other banks' risky projects. The value of each bank's project may suddenly decline depending on their cash reserves and both the occurence and magnitude of liquidity shocks. In two distinct settings, we solve the system-wide optimal control problem and obt…
The problem of portfolio management represents an important and challenging class of dynamic decision making problems, where rebalancing decisions need to be made over time with the consideration of many factors such as investors preferences, trading environments, and market conditions. In this paper, we present a new portfolio policy network architecture for deep reinforcement learning (DRL)that can exploit more eff…
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…
We analyse the effect of a proportional wealth tax on asset returns, portfolio choice, and asset pricing. The tax is levied annually on the market value of all holdings at a uniform rate. We show that such a tax is economically equivalent to the government acquiring a proportional stake in the investor's portfolio each period -- a form of risk sharing in which expected wealth and risk are reduced by the same factor, …
Fractional-reserve banking is taking deposits and holding only a fraction in reserves or liquid assets — credit creation with a run risk.
A reserve requirement is the fraction of deposits a bank must hold as reserves — a tool that is now often zero in the US, with liquidity rules doing the real work.
A stablecoin is a token that targets a peg, usually $1 — a money-market claim or an algorithmic hope, depending on the reserves.
Mid-September 2019 US GC/SOFR printed in the double digits for a day as reserves met a tax date and bill supply — a plumbing scare that created the standing repo facility debate.
A peg is a policy that holds the exchange rate to a target or band — a promise that spends reserves and rates when the market disagrees.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
Bank reserve balances reflect the quantity of reserves held by banks at the Federal Reserve and are central to understanding liquidity distribution and financial system stability.
The Fed balance sheet reflects the scale of Federal Reserve asset holdings and is a major driver of reserves, liquidity conditions, and policy transmission.
QT pace refers to the speed at which the Federal Reserve allows assets to roll off its balance sheet, affecting reserves, duration supply, and market liquidity.
Reverse Repo Facility usage shows how much cash is being parked at the Federal Reserve overnight and helps track reserve distribution, collateral demand, and system liquidity conditions.
Treasury General Account tracks the U.S. Treasury’s cash balance at the Federal Reserve and influences system liquidity by absorbing or releasing reserves.
Monetary policy is the central bank’s control of short rates, liquidity, and sometimes the balance sheet — the price of reserves and the path of the front end.
Quantitative easing is large-scale central-bank asset purchases that expand reserves — a duration and liquidity operation when the policy rate is pinned.
Quantitative Tightening Pace — The speed of balance-sheet runoff and its impact on reserves, collateral markets, and term funding.
Bank reserve balances reflect the quantity of reserves held by banks at the Federal Reserve and are central to understanding liquidity distribution and financial system stability.
A peg is a policy that holds the exchange rate to a target or band — a promise that spends reserves and rates when the market disagrees.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
The Fed balance sheet reflects the scale of Federal Reserve asset holdings and is a major driver of reserves, liquidity conditions, and policy transmission.
Fractional-reserve banking is taking deposits and holding only a fraction in reserves or liquid assets — credit creation with a run risk.
Monetary policy is the central bank’s control of short rates, liquidity, and sometimes the balance sheet — the price of reserves and the path of the front end.
QT pace refers to the speed at which the Federal Reserve allows assets to roll off its balance sheet, affecting reserves, duration supply, and market liquidity.
Quantitative easing is large-scale central-bank asset purchases that expand reserves — a duration and liquidity operation when the policy rate is pinned.
Quantitative Tightening Pace — The speed of balance-sheet runoff and its impact on reserves, collateral markets, and term funding.
Mid-September 2019 US GC/SOFR printed in the double digits for a day as reserves met a tax date and bill supply — a plumbing scare that created the standing repo facility debate.
A reserve requirement is the fraction of deposits a bank must hold as reserves — a tool that is now often zero in the US, with liquidity rules doing the real work.
A stablecoin is a token that targets a peg, usually $1 — a money-market claim or an algorithmic hope, depending on the reserves.
Treasury General Account tracks the U.S. Treasury’s cash balance at the Federal Reserve and influences system liquidity by absorbing or releasing reserves.