Quantitative Finance

Dolinsky, Yan

doi: 10.48550/arxiv.2210.03917pmid: N/A

Abstract: In this paper, we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the duality, we treat utility-based hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute explicitly the optimal trading strategy.

Tann, Wesley Joon-Wie;Vuputuri, Akhil;Chang, Ee-Chien

doi: N/Apmid: N/A

Abstract: Non-fungible tokens (NFTs) are digital assets stored on a blockchain representing real-world objects such as art or collectibles. An NFT collection comprises numerous tokens; each token can be transacted multiple times. It is a multibillion-dollar market where the number of collections has more than doubled in 2022. In this paper, we want to obtain a generative model that, given the early transactions history (first quarter Q1) of a newly minted collection, generates subsequent transactions (quarters Q2, Q3, Q4), where the generative model is trained using the transaction history of a few mature collections. The goal is to use the generated transactions to project the potential market value of this newly minted collection over the next few quarters. A technical challenge exists in that different collections have diverse characteristics, and the generative model should generate based on the appropriate "contexts" of the collection. Our method takes a two-step approach. First, it employs unsupervised learning on the early transactions to extract characteristics (which we call contexts) of NFT collections. Next, it generates future transactions of each token based on these contexts and the early transactions, projecting the target collection's potential market value. Comprehensive experiments demonstrate our contextual generative approach's NFT projection capabilities.

Sun, Xiaotong;Chen, Xi;Stasinakis, Charalampos;Sermpinis, Georgios

doi: N/Apmid: N/A

Abstract: Decentralized Autonomous Organization (DAO) provides a decentralized governance solution through blockchain, where decision-making process relies on on-chain voting and follows majority rule. This paper focuses on MakerDAO, and we find five voter coalitions after applying clustering algorithm to voting history. The emergence of a dominant voter coalition is a signal of governance centralization in DAO, and voter coalitions have complicated influence on Maker protocol, which is governed by MakerDAO. This paper presents empirical evidence of multicoalition democracy in DAO and further contributes to the contemporary debate on whether decentralized governance is possible.

Rodriguez-Cruz, Clary;Molaei, Mehdi;Thirumalaiswamy, Amruthesh;Feitosa, Klebert;Manoharan, Vinothan N.;Sivarajan, Shankar;Reich, Daniel H.;Riggleman, Robert A.;Crocker, John C.

doi: 10.48550/arxiv.2210.13667pmid: N/A

Abstract: Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively reproduces the high-dimensional fractal geometry of the configuration path and its associated energy minima generated using a computational model. That geometry in turn drives the droplets' complex random motion observed in real space. Our results indicate that experimental studies can elucidate whether the similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.

Gietzmann, Miles B.;Ostaszewski, Adam J.

doi: N/Apmid: N/A

Abstract: In a continuous-time setting we investigate how the management of a firm controls a dynamic choice between two generic voluntary disclosure decision rules: one with full and transparent disclosure termed $\it{candid}$, the other, termed $\it{sparing}$, under which values only above a dynamic threshold are disclosed. We show how management are rewarded with a reputational premium for candour. The candid strategy is costly because the sparing alternative shields the firm from potential downgrades following low value disclosures. We show how parameters of the model such as news intensity, pay-for-performance and time-to-mandatory-disclosure determine the optimal choice of candid versus sparing strategy and the optimal time for management to switch between the two. The private news updates received by management are modelled with a Poisson process, occurring between the fixed mandatory disclosure dates, such as fiscal years or quarters, with the news received generated by a background Black-Scholes model of economic activity and of its partial observation. The model presented develops a number of insights, based on a very simple ordinary differential equation (ODE) characterizing equilibrium in a piecewise-deterministic model, derivable from the background Black-Scholes model. It is shown that in equilibrium when news intensity is low a firm may employ a candid disclosure strategy throughout, but will otherwise switch (alternate) between periods of being candid and periods of being sparing with the truth (or the other way about); that is, we are able to characterize when in equilibrium a candid firm will switch to adopting a sparing strategy. The model illustrates how parameters such as time to mandatory disclosure, news intensity and pay-for-performance may drive such switching behaviour. $\it{With\,constant\,pay\,for\,performance\,parameters,\,at\,most\,one\, switching\,occurs.}$

Kapengut, Elie;Mizrach, Bruce

doi: N/Apmid: N/A

Abstract: On September 15, 2022, the Ethereum network adopted a proof-of-stake (PoS) consensus mechanism. We study the impact on the network and competing platforms in a two month event window around the Beacon chain merge. We find that the transition to PoS has reduced energy consumption by 99.98%. Miners have not transformed into validators, and total block reward income (in USD) has fallen by 97%, though transaction fees (in ETH) for Ether have increased nearly 10%. The Herfindahl index for the top 10 is 1,009; the network is 19% less concentrated after the merge. Ethereum supply growth has been deflationary since the merge. The time between consecutive blocks is now steady at 12 seconds and transactions per day are up 7.0%. On Polygon, Matic fees rose but token fees fell. Polygon also slows, processing 3.3% fewer transactions per day. Solana's fees fall by $0.0003, and transactions per day are down 48%. Stablecoin transfer volumes fall on Ethereum and Polygon, but rise on Solana.

Cont, Rama;Micheli, Alessandro;Neuman, Eyal

doi: 10.48550/arxiv.2210.01901pmid: N/A

Abstract: We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.

Nendel, Max

doi: N/Apmid: N/A

Abstract: The main result of this paper characterizes the continuity from below of monotone functionals on the space $C_b$ of bounded continuous functions on an arbitrary Polish space as lower semicontinuity in the mixed topology. The mixed topology is the Mackey topology for the dual pair $(C_b,{\rm ca})$, where ${\rm ca}$ denotes the space of all countably additive signed Borel measures of finite variation. As such, lower semicontinuity in the mixed topology of convex monotone maps $C_b\to \mathbb R$ is equivalent to a dual representation in terms of countably additive measures. Such representations are of fundamental importance, e.g., in the context of risk measures and super hedging problems. Another main result of this paper provides a characterization of equicontinuity in the mixed topology for families of convex monotone maps. As a consequence, for every convex monotone map on $C_b$ taking values in a locally convex vector lattice, continuity in the mixed topology is equivalent to continuity on norm bounded sets.

Wei, Yunran;Zitikis, Ricardas

doi: 10.48550/arxiv.2210.16880pmid: N/A

Abstract: This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various perspectives. The invention helps to avoid a number of technical assumptions that have been traditionally imposed when working with quantities containing quantiles. In particular it helps to completely avoid the requirement of the existence of a probability density function. The developed results explain and illustrate the invention, whose byproducts include the assessment of model uncertainty and misspecification, and the derivation of statistical inference results.

Guan, Guohui;Liang, Zongxia;Song, Yilun

doi: N/Apmid: N/A

Abstract: This paper studies the continuous-time pre-commitment KMM problem proposed by Klibanoff, Marinacci and Mukerji (2005) in incomplete financial markets, which concerns with the portfolio selection under smooth ambiguity. The decision maker (DM) is uncertain about the dominated priors of the financial market, which are characterized by a second-order distribution (SOD). The KMM model separates risk attitudes and ambiguity attitudes apart and the aim of the DM is to maximize the two-fold utility of terminal wealth, which does not belong to the classical subjective utility maximization problem. By constructing the efficient frontier, the original KMM problem is first simplified as an one-fold expected utility problem on the second-order space. In order to solve the equivalent simplified problem, this paper imposes an assumption and introduces a new distorted Legendre transformation to establish the bipolar relation and the distorted duality theorem. Then, under a further assumption that the asymptotic elasticity of the ambiguous attitude is less than 1, the uniqueness and existence of the solution to the KMM problem are shown and we obtain the semi-explicit forms of the optimal terminal wealth and the optimal strategy. Explicit forms of optimal strategies are presented for CRRA, CARA and HARA utilities in the case of Gaussian SOD in a Black-Scholes financial market, which show that DM with higher ambiguity aversion tends to be more concerned about extreme market conditions with larger bias. In the end of this work, numerical comparisons with the DMs ignoring ambiguity are revealed to illustrate the effects of ambiguity on the optimal strategies and value functions.