scholarly journals SPX Calibration of Option Approximations under Rough Heston Model

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2675
Author(s):  
Siow Woon Jeng ◽  
Adem Kiliçman
Keyword(s):  
Brownian Motion ◽  
Numerical Study ◽  
Computational Cost ◽  
Option Price ◽  
Padé Approximant ◽  
Heston Model ◽  
Approximation Formula ◽  
Approximation Methods ◽  
Pade Approximant ◽  
Before And After

The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also known as rough Heston model has been derived as the macroscopic level of microscopic Hawkes process where it acts as a high-frequency price process. Unlike the pricing of options under the classical Heston model, it is significantly harder to price options under rough Heston model due to the large computational cost needed. Previously, some studies have proposed a few approximation methods to speed up the option computation. In this study, we calibrate five different approximation methods for pricing options under rough Heston model to SPX options, namely a third-order Padé approximant, three variants of fourth-order Padé approximant, and an approximation formula made from decomposing the option price. The main purpose of this study is to fill in the gap on lack of numerical study on real market options. The numerical experiment includes calibration of the mentioned methods to SPX options before and after the Lehman Brothers collapse.

Research on the American Call Options on the Stocks Paying Multiple Dividends

2019 ◽  
Vol 27 (3) ◽  
pp. 253-274
Author(s):  
Kwangil Bae
Keyword(s):  
Brownian Motion ◽  
Lower Bound ◽  
Stock Prices ◽  
Stock Price ◽  
Numerical Study ◽  
Option Price ◽  
Upper And Lower Bounds ◽  
Multivariate Normal ◽  
Call Options ◽  
Pricing Formula

Cassimon et al. (2007) propose a pricing formula of American call options under the multiple dividends by extending Roll (1977). However, because these studies investigate the option pricing formula under the escrow model, there is inconsistency for the assumption of the stock prices. This paper proposes pricing formulas of American call options under the multiple dividends and piecewise geometric Brownian motion. For the formulas, I approximate the log prices of ex-dividend dates to follow a multivariate normal distribution, and decompose the option price as a function of payoffs and exercise boundaries. Then, I obtain an upper bound of the American call options by substituting approximated log prices into the both of the payoffs and the exercise boundaries. Besides, I obtain a lower bound of the price by substituting approximated price only into the exercise boundaries. These upper and lower bounds are exact prices when the amounts of dividends are linear to the stock prices. According to the numerical study, the lower bound produces relatively small errors. Especially, it produces small errors when the dividends are more sensitive to the stock price changes.

scholarly journals Prediction of 3D Cardiovascular hemodynamics before and after coronary artery bypass surgery via deep learning

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Gaoyang Li ◽  
Haoran Wang ◽  
Mingzi Zhang ◽  
Simon Tupin ◽  
Aike Qiao ◽  
...  
Keyword(s):  
Deep Learning ◽  
Artery Bypass ◽  
Computational Cost ◽  
Specific Model ◽  
Arterial System ◽  
Patient Specific ◽  
Cardiovascular Hemodynamics ◽  
Before And After ◽  
Deep Learning Network ◽  
Cfd Method

AbstractThe clinical treatment planning of coronary heart disease requires hemodynamic parameters to provide proper guidance. Computational fluid dynamics (CFD) is gradually used in the simulation of cardiovascular hemodynamics. However, for the patient-specific model, the complex operation and high computational cost of CFD hinder its clinical application. To deal with these problems, we develop cardiovascular hemodynamic point datasets and a dual sampling channel deep learning network, which can analyze and reproduce the relationship between the cardiovascular geometry and internal hemodynamics. The statistical analysis shows that the hemodynamic prediction results of deep learning are in agreement with the conventional CFD method, but the calculation time is reduced 600-fold. In terms of over 2 million nodes, prediction accuracy of around 90%, computational efficiency to predict cardiovascular hemodynamics within 1 second, and universality for evaluating complex arterial system, our deep learning method can meet the needs of most situations.

K+p scattering with unitary Padé approximant

1975 ◽  
Vol 87 (3) ◽  
pp. 485-508 ◽  
Author(s):  
Sarah C.B. Andrade ◽  
Erasmo Ferreira ◽  
Luis Ye Chang
Keyword(s):  
Padé Approximant ◽  
Pade Approximant

scholarly journals HOLDER-EXTENDIBLE EUROPEAN OPTION: CORRECTIONS AND EXTENSIONS

2015 ◽  
Vol 56 (4) ◽  
pp. 359-372 ◽  
Author(s):  
PAVEL V. SHEVCHENKO
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Real Life ◽  
Option Price ◽  
Geometric Brownian Motion ◽  
Fixed Amount ◽  
Underlying Asset ◽  
Closed Form Solutions ◽  
Pricing Options ◽  
Interest Rate Volatility

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.

scholarly journals A generalization of the Padé approximant

1967 ◽  
Vol 20 (3) ◽  
pp. 416-420 ◽  
Author(s):  
J.L Gammel ◽  
C.C Rousseau ◽  
D.P Saylor
Keyword(s):  
Padé Approximant ◽  
Pade Approximant

Padé Approximant Calculation of p-Wave π–π Scattering with a σ Model Lagrangian

1971 ◽  
Vol 49 (3) ◽  
pp. 360-366
Author(s):  
D. K. Elias
Keyword(s):  
Padé Approximants ◽  
Padé Approximant ◽  
P Wave ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Wave Channel ◽  
Wave Resonance ◽  
Text Interaction ◽  
Range Of Values ◽  
D Wave

A π–π it interaction via a scalar I = 0, σ exchange is considered. The contribution of the t and u channel exchanges of the σ to the p-wave, I = 1 amplitude is calculated using Padé approximants. A p-wave resonance, interpreted as the p meson, the width of which depends on the mass of the input a meson, is found; for a certain range of values of the σ mass the ρ width compares not unfavorably with similar calculations using a [Formula: see text] interaction. However, for the range of masses considered the width is considerably smaller than the experimental value. The I = 0, d-wave channel is also considered and a resonance, interpreted as the ƒ0(1260), is found.

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

Heat Transfer ◽  
2022 ◽  
Author(s):  
R. S. Varun Kumar ◽  
I. E. Sarris ◽  
G. Sowmya ◽  
J. K. Madhukesh ◽  
B. C. Prasannakumara
Keyword(s):  
Electromagnetic Field ◽  
Thermal Performance ◽  
Padé Approximant ◽  
Porous Fin ◽  
Pade Approximant

Pade approximant ELF VED fields in the Earth‐Ionosphere cavity

Radio Science ◽  
2021 ◽  
Author(s):  
PengFei Liang ◽  
QingYun Di ◽  
JianBao Fan ◽  
Ruo Wang ◽  
Ya Gao
Keyword(s):  
Padé Approximant ◽  
Pade Approximant ◽  
The Earth
Sign in / Sign up

Export Citation Format

Share Document