Monte Carlo Method

Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models ArXiv ID: 2505.00255 “View on arXiv” Authors: Takuji Arai Abstract We develop a numerical method for locally risk-minimizing (LRM) strategies for Barndorff-Nielsen and Shephard (BNS) models. Arai et al. (2017) derived a mathematical expression for LRM strategies in BNS models using Malliavin calculus for Lévy processes and presented some numerical results only for the case where the asset price process is a martingale. Subsequently, Arai and Imai (2024) developed the first Monte Carlo (MC) method available for non-martingale BNS models with infinite active jumps. Here, we modify the expression obtained by Arai et al. (2017) into a numerically tractable form, and, using the MC method developed by Arai and Imai (2024), propose a numerical method of LRM strategies available for non-martingale BNS models with infinite active jumps. In the final part of this paper, we will conduct some numerical experiments. ...

Phase Transitions in Financial Markets Using the Ising Model: A Statistical Mechanics Perspective ArXiv ID: 2504.19050 “View on arXiv” Authors: Bruno Giorgio Abstract This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features: volatility clustering, negative skewness, heavy tails, the absence of autocorrelation in returns, and the presence of autocorrelation in absolute returns. A significant portion of the dissertation is dedicated to Ising model-based simulations. Due to the lack of an analytical or deterministic solution, the Monte Carlo method was employed to explore the model’s statistical properties. The results demonstrate that the Ising model is capable of replicating the majority of the statistical features analyzed. ...

A pure dual approach for hedging Bermudan options ArXiv ID: 2404.18761 “View on arXiv” Authors: Unknown Abstract This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a “purely dual” algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency. ...

Optimizing Investment Strategies with Lazy Factor and Probability Weighting: A Price Portfolio Forecasting and Mean-Variance Model with Transaction Costs Approach ArXiv ID: 2306.07928 “View on arXiv” Authors: Unknown Abstract Market traders often engage in the frequent transaction of volatile assets to optimize their total return. In this study, we introduce a novel investment strategy model, anchored on the ’lazy factor.’ Our approach bifurcates into a Price Portfolio Forecasting Model and a Mean-Variance Model with Transaction Costs, utilizing probability weights as the coefficients of laziness factors. The Price Portfolio Forecasting Model, leveraging the EXPMA Mean Method, plots the long-term price trend line and forecasts future price movements, incorporating the tangent slope and rate of change. For short-term investments, we apply the ARIMA Model to predict ensuing prices. The Mean-Variance Model with Transaction Costs employs the Monte Carlo Method to formulate the feasible region. To strike an optimal balance between risk and return, equal probability weights are incorporated as coefficients of the laziness factor. To assess the efficacy of this combined strategy, we executed extensive experiments on a specified dataset. Our findings underscore the model’s adaptability and generalizability, indicating its potential to transform investment strategies. ...