arXiv subjects

Jaehyuk Choi

Publications and source records attributed to Jaehyuk Choi.

At least 19 recordsLinked to original sources

arXiv2025

Efficient and accurate simulation of the stochastic-alpha-beta-rho model

We propose an efficient, accurate and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) integrated variance conditional on terminal volatility and (ii) terminal forward price conditional on terminal volatility and integrated variance. For the first sampling procedure, we sample the conditional integrated variance using the moment-matched shifted lognormal approximation. For the second sampling procedure, we approximate the conditional terminal forward price as a constant-elasticity-of-variance (CEV) distribution. Our CEV approximation preserves the martingale condition and precludes arbitrage, which is a key advantage over Islah's approximation used in most SABR simulation schemes in the literature. We then adopt the exact sampling method of the CEV distribution based on the shifted-Poisson mixture Gamma random variable. Our enhanced procedures avoid the tedious Laplace inversion algorithm for sampling integrated variance and non-efficient inverse transform sampling of the forward price in some of the earlier simulation schemes. Numerical results demonstrate our simulation scheme to be highly efficient, accurate, and reliable.

q-fin.CP↗

arXiv2024

Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding

Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton-Raphson algorithm, whose convergence is slow for extreme option prices.

q-fin.MF↗

arXiv2024

Leave-one-out least squares Monte Carlo algorithm for pricing Bermudan options

The least squares Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing Bermudan options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of avoiding it requires additional simulation paths. We present the leave-one-out LSM (LOOLSM) algorithm to eliminate look-ahead bias without doubling simulations. We also show that look-ahead bias is asymptotically proportional to the regressors-to-paths ratio. Our findings are demonstrated with several option examples in which the LSM algorithm overvalues the options. The LOOLSM method can be extended to other regression-based algorithms that improve the LSM method.

q-fin.CP↗

arXiv2024

Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo\`eve expansions

This study proposes a fast exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Lo\`eve expansions, the stochastic volatility path (Ornstein-Uhlenbeck process) is expressed as a sine series, and the time integrals of volatility and variance are analytically derived as infinite series of independent normal random variables. The new method is several hundred times faster than the existing method using numerical transform inversion. The simulation variance is further reduced with conditional simulation and the control variate.

q-fin.CP↗

arXiv2023

Simulation schemes for the Heston model with Poisson conditioning

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the modified Bessel function, based on the observation that the conditional integrated variance can be simplified when conditioned by the Poisson variate used for simulating the terminal variance. Our approach also enhances the low-bias and time discretization schemes, which are suitable for pricing derivatives with frequent monitoring. Extensive numerical tests reveal the good performance of the new simulation schemes in terms of accuracy, efficiency, and reliability when compared with existing methods.

q-fin.MF↗

arXiv2023

Information extraction and artwork pricing

Traditional art pricing models often lack fine measurements of painting content. This paper proposes a new content measurement: the Shannon information quantity measured by the singular value decomposition (SVD) entropy of the painting image. Using a large sample of artworks' auction records and images, we show that the SVD entropy positively affects the sales price at 1% significance level. Compared to the other commonly adopted content variables, the SVD entropy has advantages in variable significance, sample robustness as well as model fit. Considering the convenient availability of digital painting images and the straightforward calculation algorithm of this measurement, we expect its wide application in future research.

q-fin.PR↗

arXiv2023

CRAFT: Criticality-Aware Fault-Tolerance Enhancement Techniques for Emerging Memories-Based Deep Neural Networks

Deep Neural Networks (DNNs) have emerged as the most effective programming paradigm for computer vision and natural language processing applications. With the rapid development of DNNs, efficient hardware architectures for deploying DNN-based applications on edge devices have been extensively studied. Emerging Non-Volatile Memories (NVMs), with their better scalability, non-volatility and good read performance, are found to be promising candidates for deploying DNNs. However, despite the promise, emerging NVMs often suffer from reliability issues such as stuck-at faults, which decrease the chip yield/memory lifetime and severely impact the accuracy of DNNs. A stuck-at cell can be read but not reprogrammed, thus, stuck-at faults in NVMs may or may not result in errors depending on the data to be stored. By reducing the number of errors caused by stuck-at faults, the reliability of a DNN-based system can be enhanced. This paper proposes CRAFT, i.e., Criticality-Aware Fault-Tolerance Enhancement Techniques to enhance the reliability of NVM-based DNNs in the presence of stuck-at faults. A data block remapping technique is used to reduce the impact of stuck-at faults on DNNs accuracy. Additionally, by performing bit-level criticality analysis on various DNNs, the critical-bit positions in network parameters that can significantly impact the accuracy are identified. Based on this analysis, we propose an encoding method which effectively swaps the critical bit positions with that of non-critical bits when more errors (due to stuck-at faults) are present in the critical bits.

cs.AR↗

arXiv2023

Option pricing under the normal SABR model with Gaussian quadratures

The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options trading. In particular, the normal ($β=0$) SABR model is a popular model choice for interest rates because it allows negative asset values. The option price and delta under the SABR model are typically obtained via asymptotic implied volatility approximation, but these are often inaccurate and arbitrageable. Using a recently discovered price transition law, we propose a Gaussian quadrature integration scheme for price options under the normal SABR model. The compound Gaussian quadrature sum over only 49 points can calculate a very accurate price and delta that are arbitrage-free.

q-fin.PR↗

arXiv2022

Improved iterative methods for solving risk parity portfolio

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. We enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. We also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.

q-fin.PM↗

arXiv2022

A Black-Scholes user's guide to the Bachelier model

To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges temporarily switched the option model from Black--Scholes to Bachelier in 2020. This study reviews the literature on Bachelier's pioneering option pricing model and summarizes the practical results on volatility conversion, risk management, stochastic volatility, and barrier options pricing to facilitate the model transition. In particular, using the displaced Black-Scholes model as a model family with the Black-Scholes and Bachelier models as special cases, we not only connect the two models but also present a continuous spectrum of model choices.

q-fin.MF↗

arXiv2022

LTC-GIF: Attracting More Clicks on Feature-length Sports Videos

This paper proposes a lightweight method to attract users and increase views of the video by presenting personalized artistic media -- i.e, static thumbnails and animated GIFs. This method analyzes lightweight thumbnail containers (LTC) using computational resources of the client device to recognize personalized events from full-length sports videos. In addition, instead of processing the entire video, small video segments are processed to generate artistic media. This makes the proposed approach more computationally efficient compared to the baseline approaches that create artistic media using the entire video. The proposed method retrieves and uses thumbnail containers and video segments, which reduces the required transmission bandwidth as well as the amount of locally stored data used during artistic media generation. When extensive experiments were conducted on the Nvidia Jetson TX2, the computational complexity of the proposed method was 3.57 times lower than that of the SoA method. In the qualitative assessment, GIFs generated using the proposed method received 1.02 higher overall ratings compared to the SoA method. To the best of our knowledge, this is the first technique that uses LTC to generate artistic media while providing lightweight and high-performance services even on resource-constrained devices.

cs.CV↗

arXiv2022

Yield Spread Selection in Predicting Recession Probabilities: A Machine Learning Approach

The literature on using yield curves to forecast recessions customarily uses 10-year--three-month Treasury yield spread without verification on the pair selection. This study investigates whether the predictive ability of spread can be improved by letting a machine learning algorithm identify the best maturity pair and coefficients. Our comprehensive analysis shows that, despite the likelihood gain, the machine learning approach does not significantly improve prediction, owing to the estimation error. This is robust to the forecasting horizon, control variable, sample period, and oversampling of the recession observations. Our finding supports the use of the 10-year--three-month spread.

econ.EM↗

arXiv2022

The financial value of the within-government political network: Evidence from Chinese municipal corporate bonds

This paper examines the effect of the political network of Chinese municipal leaders on the pricing of municipal corporate bonds. Using municipal leaders' working experience to measure the political network, we find that this network reduces the bond issuance yield spreads by improving the credit ratings of the issuer, the local government financing vehicle. The relationship between political networks and issuance yield spreads is strengthened in areas where financial markets and legal systems are less developed.

q-fin.GN↗

arXiv2021

The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error in a way similar to the control variate method because the CEV model is the zero vol-of-vol limit of the SABR model. Moreover, the CEV volatility approximation yields a finite value at a zero strike and thus conveniently leads to a small-time asymptotics for the mass at zero. The numerical results compare favorably with the BS volatility approximations in terms of the approximation accuracy, small-strike volatility asymptotics, and no-arbitrage region.

q-fin.MF↗

arXiv2021

A note on the option price and 'Mass at zero in the uncorrelated SABR model and implied volatility asymptotics'

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using the Gauss--Hermite quadrature. We further obtain the option price by integrating the constant elasticity of variance (CEV) option prices in the same manner without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709-737]. For the uncorrelated SABR model, the new option pricing method is accurate and arbitrage-free across all strike prices.

q-fin.MF↗

arXiv2020

Inverse Gaussian quadrature and finite normal-mixture approximation of the generalized hyperbolic distribution

In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using the quadrature, the generalized hyperbolic distribution is efficiently approximated as a finite normal variance-mean mixture. Therefore, the expectations under the distribution, such as cumulative distribution function and European option price, are accurately computed as weighted sums of those under normal distributions. The generalized hyperbolic random variates are also sampled in a straightforward manner. The accuracy of the methods is illustrated with numerical examples.

stat.CO↗

arXiv2018

Hyperbolic normal stochastic volatility model

For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's $S_U$ distribution---a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the $S_U$ distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.

q-fin.MF↗

arXiv2018

Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options

Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the basket, spread, and Asian options. The option price is expressed as a quadrature integration of analytic multi-asset BSM prices under a single Brownian motion. Then the state space is rotated in such a way that the quadrature requires much coarser nodes than it would otherwise or low varying dimensions are reduced. The accuracy and efficiency of the method is illustrated through various numerical experiments.

q-fin.PR↗