Related papers: Limit order trading with a mean reverting referenc…
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…
We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the…
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…
We study super--replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constraint. The first result in this paper reveals that in reasonable…
Calibrating a trading rule using a historical simulation (also called backtest) contributes to backtest overfitting, which in turn leads to underperformance. In this paper we propose a procedure for determining the optimal trading rule…
We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or…
A consistency criterion for price impact functions in limit order markets is proposed that prohibits chain arbitrage exploitation. Both the bid-ask spread and the feedback of sequential market orders of the same kind onto both sides of the…
We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that…
This paper extends the existing drawdown modulation control policy to include a novel restart mechanism for trading. It is known that the drawdown modulation policy guarantees the maximum percentage drawdown no larger than a prespecified…
This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and…
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed…
The takeoff point of this paper is to generalize the existing stock trading results for a class of affine feedback controller to include consideration of a stop-loss order. Using the geometric Brownian motion as the underlying stock price…
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading…
Assuming that the stock price $Z=(Z_t)_{0\leq t\leq T}$ follows a geometric Brownian motion with drift $\mu\in\mathbb{R}$ and volatility $\sigma>0$, and letting $M_t=\max_{0\leq s\leq t}Z_s$ for $t\in[0,T]$, we consider the optimal…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some…
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…
We study a natural combinatorial pricing problem for sequentially arriving buyers with equal budgets. Each buyer is interested in exactly one pair of items and purchases this pair if and only if, upon arrival, both items are still available…
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.…
In order-driven markets, limit-order book (LOB) resiliency is an important microscopic indicator of market quality when the order book is hit by a liquidity shock and plays an essential role in the design of optimal submission strategies of…
A fundamental economic question is that of designing revenue-maximizing mechanisms in dynamic environments. This paper considers a simple yet compelling market model to tackle this question, where forward-looking buyers arrive at the market…