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I introduce an agent-based model of a Perpetual Futures market with heterogeneous agents trading via a central limit order book. Perpetual Futures (henceforth Perps) are financial derivatives introduced by the economist Robert Shiller, designed to peg their price to that of the underlying Spot market. This paper extends the limit order book model of Chiarella et al. (2002) by taking their agent and orderbook paramete…
Examples of stochastic processes whose state space representations involve functions of an integral type structure $$I_{t}^{(a,b)}:=\int_{0}^{t}b(Y_{s})e^{-\int_{s}^{t}a(Y_{r})dr}ds, \quad t\ge 0$$ are studied under an ergodic semi-Markovian environment described by an $S$ valued jump type process $Y:=(Y_{s}:s\in\mathbb{R}^{+})$ that is ergodic with a limiting distribution $π\in\mathcal{P}(S)$. Under different assump…
We introduce $\textbf{Slippage-at-Risk (SaR)}$, a quantitative framework for measuring liquidity risk in perpetual futures exchanges. Unlike backward-looking metrics such as Value-at-Risk computed on historical returns or realized deficit distributions, SaR provides a \emph{forward-looking} assessment of liquidation execution risk derived from current order book microstructure. The framework comprises three complemen…
This whitepaper introduces an innovative mechanism for pricing perpetual contracts and quoting fees to traders based on current market conditions. The approach employs liquidity curves and on-chain oracles to establish a new adaptive pricing framework that considers various factors, ensuring pricing stability and predictability. The framework utilizes parabolic and sigmoid functions to quote prices and fees, accounti…
The label event-linked perpetual often conflates mathematically different contracts. We replace a flat product list with a four-axis taxonomy: underlying geometry, temporal structure, settlement structure, and venue-oracle composition. The taxonomy covers a single binary probability, conditional ratios, event spreads, baskets, path functionals, liquidity indices, rolling sequences, and flow-only swaps. We derive a co…
We study permissionless spot--perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot inventory and derivative margin under on-chain liquidity and execution frictions. The paper delivers three results. First, it solves a static control problem for the collateral share and…
Perpetual swaps are derivative contracts that allow traders to speculate on, or hedge, the price movements of cryptocurrencies. Unlike futures contracts, perpetual swaps have no settlement or expiration in the traditional sense. The funding rate acts as the mechanism that tethers the perpetual swap to its underlying with the help of arbitrageurs. Open interest, in the context of perpetual swaps and derivative contrac…
Crypto-listed equity perpetuals trade while the primary cash market is closed, yet still need a mark for margin, funding, and liquidation. We model the closed-window mark as the fixed point of an oracle operator with two blocks: external anchoring and self/peer derivative reference. From marks and proxies alone the two are observationally equivalent: every reduced form admits infinitely many topology decompositions, …
Robert Shiller proposed perpetual futures in 1993 to create derivative markets for assets that are illiquid or whose price cannot be observed directly, such as single family homes, human capital, and the consumer price index. The crypto markets later built the instrument for a different reason and with a different funding rule. We give a single no arbitrage result that nests both designs: the perpetual price is the p…
Financial options are fundamental to traditional markets, enabling strategies ranging from hedging to speculating. Yet, while the Automated Market Maker paradigm has revolutionized decentralized spot markets, no equivalent standard has emerged for on-chain options. Typical designs attempt to replicate centralized exchange mechanics, requiring high-frequency oracles and robust liquidation engines which may fail during…
We study whether crypto-style perpetual-futures mechanics can be applied to a binary event claim that ultimately pays 0 or 1. A synthetic long entered at price p0 with collateral xp0/L has terminal equity -xp0(1-1/L) when the claim pays 0, if the position survives to resolution without a top-up, close, or conversion. Thus any L > 1 creates an adverse-outcome account shortfall under these conditions, independent of th…
Backtests of cryptocurrency perpetual futures are sensitive to execution timing, funding alignment, trading costs, and reuse of evaluation windows during parameter search. In high-friction markets, attractive results may therefore reflect hidden implementation choices as much as signal quality. Using BTC/USDT, ETH/USDT, SOL/USDT, and AVAX/USDT perpetual contracts, this study examines whether an auditable execution-aw…
In this paper, we analyze traders' behavior within both centralized exchanges (CEXs) and decentralized exchanges (DEXs), focusing on the volatility of Bitcoin prices and the trading activity of investors engaged in perpetual future contracts. We categorize the architecture of perpetual future exchanges into three distinct models, each exhibiting unique patterns of trader behavior in relation to trading volume, open i…
This paper investigates problems associated with the valuation of callable American volatility put options. Our approach involves modeling volatility dynamics as a mean-reverting 3/2 volatility process. We first propose a pricing formula for the perpetual American knock-out put. Under the given conditions, the value of perpetual callable American volatility put options is discussed.
In recent years, hyperparameter optimization (HPO) has become an increasingly important issue in the field of machine learning for the development of more accurate forecasting models. In this study, we explore the potential of HPO in modeling stock returns using a deep neural network (DNN). The potential of this approach was evaluated using technical indicators and fundamentals examined based on the effect the regula…
We argue that the present crisis and stalling economy continuing since 2007 are rooted in the delusionary belief in policies based on a "perpetual money machine" type of thinking. We document strong evidence that, since the early 1980s, consumption has been increasingly funded by smaller savings, booming financial profits, wealth extracted from house price appreciation and explosive debt. This is in stark contrast wi…
We study reinforcement learning (RL) on volatility surfaces through the lens of Scientific AI. We ask whether axiomatic no-arbitrage laws, imposed as soft penalties on a learned world model, can reliably align high-capacity RL agents, or mainly create Goodhart-style incentives to exploit model errors. From classical static no-arbitrage conditions we build a finite-dimensional convex volatility law manifold of admissi…
Foundation models have transformed domains from language to genomics by learning general-purpose representations from large-scale, heterogeneous data. We introduce TradeFM, a 524M-parameter generative Transformer that brings this paradigm to market microstructure, learning directly from billions of trade events across >9K equities. To enable cross-asset generalization, we develop scale-invariant features and a univer…