arXiv · arXiv q-fin · 2022
The binomial tree method and the Monte Carlo (MC) method are popular methods for solving option pricing problems. However in both methods there is a trade-off between accuracy and speed of computation, both of which are important in applications. We introduce a new method, the MC-Tree method, that combines the MC method with the binomial tree method. It employs a mixing distribution on the tree parameters, which are …
Yen Thuan Trinh, Bernard Hanzon
arXiv · arXiv q-fin · 2025
We establish a general matched filter principle for order flow normalization: optimal normalization must match the scaling behaviour of the signal-generating process. For capacity-constrained institutional investors, market capitalization normalization ($S^{MC}$) is the matched filter; for volume-targeting traders (e.g., VWAP/TWAP algorithms), trading value normalization ($S^{TV}$) is optimal. Monte Carlo simulations…
Sungwoo Kang
arXiv · arXiv q-fin · 2024
The present work addresses the challenge of training neural networks for Dynamic Initial Margin (DIM) computation in counterparty credit risk, a task traditionally burdened by the high costs associated with generating training datasets through nested Monte Carlo (MC) simulations. By condensing the initial market state variables into an input vector, determined through an interest rate model and a parsimonious paramet…
Joel P. Villarino, Álvaro Leitao
arXiv · arXiv q-fin · 2024
Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exc…
Boris Ter-Avanesov, Gunter A. Meissner
arXiv · arXiv q-fin · 2023
Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as co…
Titos Matsakos, Stuart Nield
arXiv · arXiv q-fin · 2023
This paper initiates a series of studies on a COS-tensor framework, as an efficient alternative to MC for large and liquid portfolios characterized by a modest number of dominant risk factors but a large number of trades. The framework is built on three key insights. First, the cumulative distribution function (CDF) of portfolio level mark-to-market (MtM) values and exposures can be recovered in the Fourier domain by…
Gijs Mast, Fang Fang, Xiaoyu Shen, Marnix Brands
arXiv · arXiv q-fin · 2022
Volatility clustering is a common phenomenon in financial time series. Typically, linear models can be used to describe the temporal autocorrelation of the (logarithmic) variance of returns. Considering the difficulty in estimating this model, we construct a Dynamic Bayesian Network, which utilizes the conjugate prior relation of normal-gamma and gamma-gamma, so that its posterior form locally remains unchanged at ea…
Di Zhang, Qiang Niu, Youzhou Zhou
arXiv · arXiv q-fin · 2022
Decentralized Finance (DeFi) is a nascent set of financial services, using tokens, smart contracts, and blockchain technology as financial instruments. We investigate four possible drivers of DeFi returns: exposure to cryptocurrency market, the network effect, the investor's attention, and the valuation ratio. As DeFi tokens are distinct from classical cryptocurrencies, we design a new dedicated market index, denoted…
Florentina Şoiman, Guillaume Dumas, Sonia Jimenez-Garces
arXiv · arXiv q-fin · 2021
Local volatility models usually capture the surface of implied volatilities more accurately than other approaches, such as stochastic volatility models. We present the results of application of Monte Carlo (MC) and Quasi Monte Carlo (QMC) methods for derivative pricing and risk analysis based on Hyperbolic Local Volatility Model. In high-dimensional integration QMC shows a superior performance over MC if the effectiv…
Julien Hok, Sergei Kucherenko
arXiv · arXiv q-fin · 2021
Predicting future values at risk (fVaR) is an important problem in finance. They arise in the modelling of future initial margin requirements for counterparty credit risk and future market risk VaR. One is also interested in derived quantities such as: i) Dynamic Initial Margin (DIM) and Margin Value Adjustment (MVA) in the counterparty risk context; and ii) risk weighted assets (RWA) and Capital Value Adjustment (KV…
Narayan Ganesan, Bernhard Hientzsch
arXiv · arXiv q-fin · 2019
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple non-linear financial derivatives as vanilla European optio…
Raul Merino, Jan Pospíšil, Tomáš Sobotka, Tommi Sottinen, Josep Vives
arXiv · arXiv q-fin · 2018
Sparked by Alòs, León, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models such as Heston (1993), these non-Markovian models with fractional volatility drivers allow to parsimo…
Christian Bayer, Benjamin Stemper
arXiv · arXiv q-fin · 2018
This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Malliavin calculus for the computation of Greeks: Delta, Vega, and Rho and it extends the method slightl…
Bilgi Yilmaz
arXiv · arXiv q-fin · 2018
The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied volatility surfaces. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is …
Christian Bayer, Chiheb Ben Hammouda, Raul Tempone
arXiv · arXiv q-fin · 2017
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, fo…
Seyed Amir Hejazi, Kenneth R. Jackson, Guojun Gan
arXiv · arXiv q-fin · 2016
Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, e…
Seyed Amir Hejazi, Kenneth R. Jackson
arXiv · arXiv q-fin · 2015
During recent years the counterparty risk subject has received a growing attention because of the so called Basel Accord. In particular the Basel III Accord asks the banks to fulfill finer conditions concerning counterparty credit exposures arising from banks' derivatives, securities financing transactions, default and downgrade risks characterizing the Over The Counter (OTC) derivatives market, etc. Consequently the…
M. Bonollo, L. Di Persio, I. Oliva, A. Semmoloni
arXiv · arXiv q-fin · 2014
It is important for a portfolio manager to estimate and analyze recent portfolio volatility to keep the portfolio's risk within limit. Though the number of financial instruments in the portfolio can be very large, sometimes more than thousands, daily returns considered for analysis are only for a month or even less. In this case rank of portfolio covariance matrix is less than full, hence solution is not unique. It i…
Sourish Das, Aritra Halder, Dipak K. Dey