Derivatives/Options

Risk-Neutral Pricing of Random-Expiry Options Using Trinomial Trees ArXiv ID: 2508.17014 “View on arXiv” Authors: Sebastien Bossu, Michael Grabchak Abstract Random-expiry options are nontraditional derivative contracts that may expire early based on a random event. We develop a methodology for pricing these options using a trinomial tree, where the middle path is interpreted as early expiry. We establish that this approach is free of arbitrage, derive its continuous-time limit, and show how it may be implemented numerically in an efficient manner. ...

Arbitrage with bounded Liquidity ArXiv ID: 2507.02027 “View on arXiv” Authors: Christoph Schlegel, Quintus Kilbourn Abstract We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{“two imperfectly liquid”} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our result highlights that the LVR depends on the relative liquidity and relative trading volume of the two markets between which arbitrage gains are extracted. Our model assumes that trading costs on at least one of the markets is quadratic. This assumption holds well in practice, with the exception of highly liquid major pairs on centralized exchanges, for which we discuss extensions to other cost functions. ...

Inferring Option Movements Through Residual Transactions: A Quantitative Model ArXiv ID: 2410.16563 “View on arXiv” Authors: Unknown Abstract This research presents a novel approach to predicting option movements by analyzing residual transactions, which are trades that deviate from standard hedging activities. Unlike traditional methods that primarily focus on open interest and trading volume, this study argues that residuals can reveal nuanced insights into institutional sentiment and strategic positioning. By examining these deviations, the model identifies early indicators of market trends, providing a refined framework for forecasting option prices. The proposed model integrates classical machine learning and regression techniques to analyze patterns in high frequency trading data, capturing complex, non linear relationships. This predictive framework allows traders to anticipate shifts in option values, enhancing strategies for better market timing, risk management, and portfolio optimization. The model’s adaptability, driven by real time data processing, makes it particularly effective in fast paced trading environments, where early detection of institutional behavior is crucial for gaining a competitive edge. Overall, this research contributes to the field of options trading by offering a strategic tool that detects early market signals, optimizing trading decisions based on predictive insights derived from residual trading patterns. This approach bridges the gap between conventional metrics and the subtle behaviors of institutional players, marking a significant advancement in options market analysis. ...

Rank-Dependent Predictable Forward Performance Processes ArXiv ID: 2403.16228 “View on arXiv” Authors: Unknown Abstract Predictable forward performance processes (PFPPs) are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead. This is a common scenario in which a controlling agent frequently re-calibrates her model. We introduce a new class of PFPPs based on rank-dependent utility, generalizing existing models that are based on expected utility theory (EUT). We establish existence of rank-dependent PFPPs under a conditionally complete market and exogenous probability distortion functions which are updated periodically. We show that their construction reduces to solving an integral equation that generalizes the integral equation obtained under EUT in previous studies. We then propose a new approach for solving the integral equation via theory of Volterra equations. We illustrate our result in the special case of conditionally complete Black-Scholes model. ...