arXiv subjects

Alexander Lipton

Publications and source records attributed to Alexander Lipton.

At least 19 recordsLinked to original sources

arXiv2026

Towards Decentralized Registries for Assets Metadata Information

The effort to tokenize non-currency assets faces several hurdles, including the lack of a scalable decentralized computing infrastructure to manage asset-related metadata. While the centralized securities depository model has served the financial industry well for several decades, the vision of tokenization at a global scale requires new infrastructure that enables distributed control while protecting the integrity of asset-related metadata, regardless of where it is stored. In this paper, we discuss the decentralized artifacts metadata registry model for tokenized assets as a possible direction for the financial industry seeking to embrace tokenization. The artifacts metadata registries extend the function of the traditional CSD, and could in fact be a new type of service offered by CSDs around the world.

cs.DC↗

arXiv2024

Unified Approach for Hedging Impermanent Loss of Liquidity Provision

We develop static and dynamic approaches for hedging of the impermanent loss (IL) of liquidity provision (LP) staked at Decentralised Exchanges (DEXes) which employ Uniswap V2 and V3 protocols. We provide detailed definitions and formulas for computing the IL to unify different definitions occurring in the existing literature. We show that the IL can be seen a contingent claim with a non-linear payoff for a fixed maturity date. Thus, we introduce the contingent claim termed as IL protection claim which delivers the negative of IL payoff at the maturity date. We apply arbitrage-based methods for valuation and risk management of this claim. First, we develop the static model-independent replication method for the valuation of IL protection claim using traded European vanilla call and put options. We extend and generalize an existing method to show that the IL protection claim can be hedged perfectly with options if there is a liquid options market. Second, we develop the dynamic model-based approach for the valuation and hedging of IL protection claims under a risk-neutral measure. We derive analytic valuation formulas using a wide class of price dynamics for which the characteristic function is available under the risk-neutral measure. As base cases, we derive analytic valuation formulas for IL protection claim under the Black-Scholes-Merton model and the log-normal stochastic volatility model. We finally discuss estimation of risk-reward of LP staking using our results.

q-fin.MF↗

arXiv2024

A Geometric Approach To Asset Allocation With Investor Views

In this article, a geometric approach to incorporating investor views in portfolio construction is presented. In particular, the proposed approach utilizes the notion of generalized Wasserstein barycenter (GWB) to combine the statistical information about asset returns with investor views to obtain an updated estimate of the asset drifts and covariance, which are then fed into a mean-variance optimizer as inputs. Quantitative comparisons of the proposed geometric approach with the conventional Black-Litterman model (and a closely related variant) are presented. The proposed geometric approach provides investors with more flexibility in specifying their confidence in their views than conventional Black-Litterman model-based approaches. The geometric approach also rewards the investors more for making correct decisions than conventional BL based approaches. We provide empirical and theoretical justifications for our claim.

q-fin.MF↗

arXiv2024

Hydrodynamics of Markets:Hidden Links Between Physics and Finance

An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equations, the Ornstein-Uhlenbeck and Feller processes, and their generalizations. They are reduced to affine differential and pseudo-differential equations and solved in a unified way by using Kelvin waves and developing a comprehensive math framework for calculating transition probabilities and expectations. Kelvin waves are instrumental for studying the well-known Black-Scholes, Heston, and Stein-Stein models and more complex path-dependent volatility models, as well as the pricing of Asian options, volatility and variance swaps, bonds, and bond options. Kelvin waves help to solve several cutting-edge problems, including hedging the impermanent loss of Automated Market Makers for cryptocurrency trading. This title is also available as Open Access on Cambridge Core.

q-fin.MF↗

arXiv2023

Kelvin Waves, Klein-Kramers and Kolmogorov Equations, Path-Dependent Financial Instruments: Survey and New Results

We discover several surprising relationships between large classes of seemingly unrelated foundational problems of financial engineering and fundamental problems of hydrodynamics and molecular physics. Solutions in all these domains can be reduced to solving affine differential equations commonly used in various mathematical and scientific disciplines to model dynamic systems. We have identified connections in these seemingly disparate areas as we link together small wave-like perturbations of linear flows in ideal and viscous fluids described in hydrodynamics by Kevin waves to motions of free and harmonically bound particles described in molecular physics by Klein-Kramers and Kolmogorov equations to Gaussian and non-Gaussian affine processes, e.g., Ornstein-Uhlenbeck and Feller, arising in financial engineering. To further emphasize the parallels between these diverse fields, we build a coherent mathematical framework using Kevin waves to construct transition probability density functions for problems in hydrodynamics, molecular physics, and financial engineering. As one of the outcomes of our analysis, we discover that the original solution of the Kolmogorov equation contains an error, which we subsequently correct. We apply our interdisciplinary approach to advance the understanding of various financial engineering topics, such as pricing of Asian options, volatility and variance swaps, options on stocks with path-dependent volatility, bonds, and bond options. We also discuss further applications to other exciting problems of financial engineering.

q-fin.MF↗

arXiv2023

SPX, VIX and scale-invariant LSV\footnote{Local Stochastic Volatility}

Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data. However, the literature misses a potent approach commonly used in physics and works with absolute (dimensional) variables rather than with relative (non-dimensional) ones. While model parameters defined in absolute terms are counter-intuitive for trading desks and tend to be heavily time-dependent, relative parameters are intuitive and stable, making it easy to steer the model adequately and consistently with its Profit and Loss (PnL) explanation power. We propose a specification that first explores historical data and uses physically well-defined relative quantities to design the model. We then develop an efficient hybrid method to price derivatives under this specification. We also show how our method can be used for robust scenario generation purposes - an important risk management task vital for buy-side firms.\footnote{The authors would like to thank Prof. Marcos Lopez de Prado and Dr. Vincent Davy Zoonekynd for valuable comments.}

q-fin.MF↗

arXiv2022

Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility

We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach to barrier options valuation utilizes two loops. First we run the outer loop by generating volatility paths via the Monte Carlo method. Second, we condition the price dynamics on a given volatility path and apply the method of heat potentials to solve the conditional problem in closed-form in the inner loop. We illustrate the accuracy and efficacy of our semi-analytical approach by comparing it with the two-dimensional Monte Carlo simulation and a hybrid method, which combines the finite-difference technique for the inner loop and the Monte Carlo simulation for the outer loop. We apply our method for computation of state probabilities (Green function), survival probabilities, and values of call options with barriers. Our approach provides better accuracy and is orders of magnitude faster than the existing methods. s a by-product of our analysis, we generalize Willard's (1997) conditioning formula for valuation of path-independent options to path-dependent options and derive a novel expression for the joint probability density for the value of drifted Brownian motion and its running minimum.

q-fin.CP↗

arXiv2021

Multilayer heat equations and their solutions via oscillating integral transforms

By expanding the Dirac delta function in terms of the eigenfunctions of the corresponding Sturm-Liouville problem, we construct some new (oscillating) integral transforms. These transforms are then used to solve various finance, physics, and mathematics problems, which could be characterized by the existence of a multilayer spatial structure and moving (time-dependent) boundaries (internal interfaces) between the layers. Thus, constructed solutions are semi-analytical and extend the authors' previous work (Itkin, Lipton, Muravey, Multilayer heat equations: application to finance, FMF, 1, 2021). However, our new method doesn't duplicate the previous one but provides alternative representations of the solution which have different properties and serve other purposes.

q-fin.PR↗

arXiv2021

Cryptocurrencies and the Future of Money

We review different classes of cryptocurrencies with emphasis on their economic properties. Pure-asset coins such as Bitcoin, Ethereum and Ripple are characterized by not being a liability of any economic agent and most resemble commodities such as gold. Central bank digital currencies, at the other end of the economic spectrum, are liabilities of a Central Bank and most resemble cash. In between, there exist a range of so-called stable coins, with varying degrees of economic complexity. We use balance sheet operations to highlight the properties of each class of cryptocurrency and their potential uses. In addition, we propose the basic structure for a macroeconomic model incorporating all the different types of cryptocurrencies under consideration.

econ.GN↗

arXiv2020

Towards a Contract Service Provider Model for Virtual Assets and VASPs

We introduce the contract service provider (CSP) model as an analog of the successful Internet ISP model. Our exploration is motivated by the need to seek alternative blockchain service-fee models that departs from the token-for-operations (gas fee) model for smart contracts found on many popular blockchain platforms today. A given CSP community consisting of multiple CSP business entities (VASPs) form a contract domain which implement well-defined contract primitives, policies and contract-ledger. The nodes of the members of CSP community form the blockchain network. We discuss a number of design principles borrowed from the design principles of the Internet Architecture, and we discuss the interoperability of cross-domain (cross-chain) transfers of virtual assets in the context of contract domains.

cs.CR↗

arXiv2020

Wallet Attestations for Virtual Asset Service Providers and Crypto-Assets Insurance

The emerging virtual asset service providers (VASP) industry currently faces a number of challenges related to the Travel Rule, notably pertaining to customer personal information, account number and cryptographic key information. VASPs will be handling virtual assets of different forms, where each may be bound to different private-public key pairs on the blockchain. As such, VASPs also face the additional problem of the management of its own keys and the management of customer keys that may reside in a customer wallet. The use of attestation technologies as applied to wallet systems may provide VASPs with suitable evidence relevant to the Travel Rule regarding cryptographic key information and their operational state. Additionally, wallet attestations may provide crypto-asset insurers with strong evidence regarding the key management aspects of a wallet device, thereby providing the insurance industry with measurable levels of assurance that can become the basis for insurers to perform risk assessment on crypto-assets bound to keys in wallets, both enterprise-grade wallets and consumer-grade wallets.

cs.CR↗

arXiv2020

From Tether to Libra: Stablecoins, Digital Currency and the Future of Money

This paper provides an overview on stablecoins and introduces a novel terminology to help better identify stablecoins with truly disruptive potential. It provides a compact definition for stablecoins, identifying the unique features that make them distinct from previously known payment systems. Furthermore, it surveys the different use cases for stablecoins as well as the underlying economic incentives for creating them. Finally, it outlines critical regulatory considerations that constrain stablecoins and summarizes key factors that are driving their rapid development.

cs.CY↗

arXiv2020

Managing COVID-19 Pandemic without Destructing the Economy

We analyze an approach to managing the COVID-19 pandemic without shutting down the economy while staying within the capacity of the healthcare system. We base our analysis on a detailed heterogeneous epidemiological model, which takes into account different population groups and phases of the disease, including incubation, infection period, hospitalization, and treatment in the intensive care unit (ICU). We model the healthcare capacity as the total number of hospital and ICU beds for the whole country. We calibrate the model parameters to data reported in several recent research papers. For high- and low-risk population groups, we calculate the number of total and intensive care hospitalizations, and deaths as functions of time. The main conclusion is that countries, which enforce reasonable hygienic measures on time can avoid lockdowns throughout the pandemic provided that the number of spare ICU beds per million is above the threshold of about 100. In countries where the total number of ICU beds is below this threshold, a limited period quarantine to specific high-risk groups of the population suffices. Furthermore, in the case of an inadequate capacity of the healthcare system, we incorporate a feedback loop and demonstrate that quantitative impact of the lack of ICU units on the death curve. In the case of inadequate ICU beds, full- and partial-quarantine scenarios outcomes are almost identical, making it unnecessary to shut down the whole economy. We conclude that only a limited-time quarantine of the high-risk group might be necessary, while the rest of the economy can remain operational.

q-bio.PE↗

arXiv2020

A closed-form solution for optimal mean-reverting trading strategies

When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (O-U) process. Market makers provide liquidity in an attempt to monetize this oscillation. They enter a long position when a security is priced below its estimated equilibrium level, and they enter a short position when a security is priced above its estimated equilibrium level. They hold that position until one of three outcomes occur: (1) they achieve the targeted profit; (2) they experience a maximum tolerated loss; (3) the position is held beyond a maximum tolerated horizon. All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders acting on behalf of a client must determine at what levels an order must be fulfilled. Those optimal levels can be determined by maximizing the trader's Sharpe ratio in the context of O-U processes via Monte Carlo experiments. This paper develops an analytical framework and derives those optimal levels by using the method of heat potentials.

q-fin.TR↗

arXiv2020

Old Problems, Classical Methods, New Solutions

We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in detail: (A) calibrating the default boundary in the structural default framework to a constant default intensity; (B) calculating default probability for a representative bank in the mean-field framework; (C) finding the hitting time probability density of an Ornstein-Uhlenbeck process. Several other problems, including pricing American put options and finding optimal mean-reverting trading strategies, are mentioned in passing. Besides, two non-financial applications -- the supercooled Stefan problem and the integrate-and-fire neuroscience problem -- are briefly discussed as well.

q-fin.MF↗

arXiv2020

Physics and Derivatives -- Interview Questions and Answers

Answers to interview questions sent to a selected group of former physicists working in finance. The interview will be published as part of a Special Issue on Physics and Derivatives by The Journal of Derivatives in the second half of 2020.

q-fin.GN↗

arXiv2019

Privacy-Preserving Claims Exchange Networks for Virtual Asset Service Providers

In order for VASPs to fulfill the regulatory requirements from the FATF and the Travel Rule, VASPs need access to truthful information regarding originators, beneficiaries and other VASPs involved in a virtual asset transfer instance. Additionally, in seeking data regarding subjects (individuals or organizations) VASPs are faced with privacy regulations such as the GDPR and CCPA. In this paper we a propose privacy-preserving claims issuance model that carries indicators of the provenance of the data and the algorithms used to derive the claim or assertion. This allows VASPs to obtain originator and beneficiary information without necessarily having access to the private data about these entities. Secondly we propose the use of a consortium trust network arrangement for VASPs to exchange signed claims about subjects and their public-key information or certificate.

cs.CR↗

arXiv2019

Towards a Public Key Management Framework for Virtual Assets and Virtual Asset Service Providers

The recent FATF Recommendations defines virtual assets and virtual assets service providers (VASP), and requires under the Travel Rule that originating VASPs obtain and hold required and accurate originator information and required beneficiary information on virtual asset transfers. In this paper we discuss the notion of key ownership evidence as a core part of originator and beneficiary information required by the FATF Recommendation. We discuss approaches to securely communicate the originator and beneficiary information between VASPs, and review existing standards for public key certificates as applied to VASPs and virtual asset transfers. We propose the notion of a trust network of VASPs in which originator and beneficiary information, including key ownership information, can be exchanged securely while observing individual privacy requirements.

cs.CR↗