arXiv · arXiv q-fin · 2022
Every financial crisis has caused a dual shock to the global economy. The shortage of market liquidity, such as default in debt and bonds, has led to the spread of bankruptcies, such as Lehman Brothers in 2008. Using the data for the ETFs of the S&P 500, Nasdaq 100, and Dow Jones Industrial Average collected from Yahoo Finance, this study implemented Deep Learning, Neuro Network, and Time-series to analyze the trend …
Weilin Fu, Zhuoran Li, Yupeng Zhang, Xingyou Zhou
arXiv · arXiv q-fin · 2016
Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positions of holding versus shorting such options. Here we provide a unified framework and generalize the …
Erhan Bayraktar, Zhou Zhou
arXiv · arXiv q-fin · 2015
We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (…
Erhan Bayraktar, Zhou Zhou
arXiv · arXiv q-fin · 2025
We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical innovations. First, we train a gradient-boosted ensemble to estimate the time-varying Hurst parameter H(t) from rolling windows of recent volatility data. Second, we feed these forecasts into…
Roshan Shah
arXiv · arXiv q-fin · 2025
This study applies the Hierarchical Risk Parity (HRP) portfolio allocation methodology to the NUAM market, a regional holding that integrates the markets of Chile, Colombia and Peru. As one of the first empirical analyses of HRP in this newly formed Latin American context, the paper addresses a gap in the literature on portfolio construction under cross-border, emerging market conditions. HRP leverages hierarchical c…
Gonzalo Ramirez-Carrillo, David Ortiz-Mora, Alex Aguilar-Larrotta
arXiv · arXiv q-fin · 2025
We extend the signature-based primal and dual solutions to the optimal stopping problem recently introduced in [Bayer et al.: Primal and dual optimal stopping with signatures, to appear in Finance & Stochastics 2025], by integrating deep-signature and signature-kernel learning methodologies. These approaches are designed for non-Markovian frameworks, in particular enabling the pricing of American options under rough …
Christian Bayer, Luca Pelizzari, Jia-Jie Zhu
arXiv · arXiv q-fin · 2021
This paper investigates problems associated with the valuation of callable American volatility put options. Our approach involves modeling volatility dynamics as a mean-reverting 3/2 volatility process. We first propose a pricing formula for the perpetual American knock-out put. Under the given conditions, the value of perpetual callable American volatility put options is discussed.
Hsuan-Ku Liu
arXiv · arXiv q-fin · 2016
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $π$ is given by the supremum over the prices of the American option under randomized models. That is, $π=\sup_{(c_i,Q_i)_i}\sum_ic_iφ^{Q_i}$, where $c_i \in \mathbb{R}_+$ and the martingale meas…
Erhan Bayraktar, Zhou Zhou
arXiv · arXiv q-fin · 2016
American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Am…
Olena Burkovska, Maximilian Gaß, Kathrin Glau, Mirco Mahlstedt, Wim Schoutens
arXiv · arXiv q-fin · 2014
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset price hits a certain level) is exponentially distributed. We obtain explicit optimal stopping rules in various cases one of which is interestingly complex because of an unexpected disc…
Sigurd Assing, Yufan Zhao
arXiv · arXiv q-fin · 2011
The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional expectations which arise in the Backward Dynamic Programming principle for such optimal stopping or stochastic control problems in a Markovian framework. Unfortunately, these Least-Square…
Gilles Pagès, Benedikt Wilbertz
arXiv · arXiv q-fin · 2009
In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options [1]. At the money (X= K) for American options, the expected payoff of both the call and put options is zero. Shepp investigated several stochastic optimization problems using marting…
L. M. Dieng
arXiv · arXiv q-fin · 2009
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].
Erhan Bayraktar, Constantinos Kardaras, Hao Xing
arXiv · arXiv q-fin · 2024
This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or short positions on options. Utilizing SPY options data recorded in five-minute intervals over a one-month period, we calculate key metrics such as Option Greeks and implied volati…
Sid Bhatia
arXiv · arXiv q-fin · 2018
The objective of this paper is to measure the degree of home bias (HB) within holdings portfolio and to identify their determining factors. By following literature and an international capital asset pricing model, we have chosen quite a number of susceptible factors that impact HB. This model is, hence, estimated for 20 countries, with cross-section econometrics, between 2008 and 2013. Our results show that all count…
Mounira Chniguir, Mohamed Kefi, Jamel Henchiri
arXiv · arXiv q-fin · 2022
When trading American and Asian options in the FX derivatives market, banks must calculate prices using a complex mathematical model. It is often observed that different models produce varying prices for the same exotic option, which violates the non-arbitrage requirement of derivative risk management. To address this issue, we have studied a fully parameterized local volatility model for pricing American/Asian optio…
Dongli Wu, Bufan Zhang, Xiao Lin
arXiv · arXiv q-fin · 2015
We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 min to 10 min. Our study is based on empirical data from the American stock market consisting of tick-…
Rafal Rak, Stanislaw Drozdz, Jaroslaw Kwapien, Pawel Oswiecimka
arXiv · arXiv q-fin · 2012
We introduce a trade strategy representation theorem for performance measurement and portable alpha in high frequency trading, by embedding a robust trading algorithm that describe portfolio manager market timing behavior, in a canonical multifactor asset pricing model. First, we present a spectral test for market timing based on behavioral transformation of the hedge factors design matrix. Second, we find that the t…
Godfrey Charles-Cadogan