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A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and…
Concentrated liquidity provision in decentralized exchanges presents a fundamental Impulse Control problem. Liquidity Providers (LPs) face a non-trivial trade-off between maximizing fee accrual through tight price-range concentration and…
This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state…
We provide further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years). Our results bolster Black's intuition that prices tend to be off roughly by a factor of 2, and take years to…
We propose a microstructural modeling framework for studying optimal market making policies in a FIFO (first in first out) limit order book (LOB). In this context, the limit orders, market orders, and cancel orders arrivals in the LOB are…
We introduce an autoregressive-type model of prices in financial market taking into account the self-modulation effect. We find that traders are mainly using strategies with weighted feedbacks of past prices. These feedbacks are responsible…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise…
In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize…
Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do…
We consider De Finetti's control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal. In order to solve this problem, we need to deal…
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which…
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
We propose a constructive framework for the super-hedging problem of a European contingent claim under proportional transaction costs in discrete time. Our main contribution is an explicit recursive scheme that computes both the…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general,…
Fundamental variables in financial market are not only price and return but a very important role is also played by trading volumes. Here we propose a new multivariate model that takes into account price returns, logarithmic variation of…
The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The…
We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the…
We propose a method based on continuous time Markov chain approximation to compute the distribution of Parisian stopping times and price Parisian options under general one-dimensional Markov processes. We prove the convergence of the method…
We study indifference pricing of exotic derivatives by using hedging strategies that take static positions in quoted derivatives but trade the underlying and cash dynamically over time. We use real quotes that come with bid-ask spreads and…