Reconstruction of the time-dependent volatility function using the Black-Scholes model
type: Item
instance of: scholarly article
title: Reconstruction of the time-dependent volatility function using the Black-Scholes model
zbMATH Open document ID: 1422.91766
DOI: 10.1155/2018/3093708
author: Yuzi Jin
author: Jian Wang
author: Sangkwon Kim
author: Youngjin Heo
author: Changwoo Yoo
author: Junseok Kim
author: Darae Jeong
author: Young Rock Kim
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: We propose a simple and robust numerical algorithm to estimate a time-dependent volatility function from a set of market observations, using the Black-Scholes (BS) model. We employ a fully implicit finite difference method to solve the BS equation numerically. To define the time-dependent volatility function, we define a cost function that is the sum of the squared errors between the market values and the theoretical values obtained by the BS model using the time-dependent volatility function. To minimize the cost function, we employ the steepest descent method. However, in general, volatility functions for minimizing the cost function are nonunique. To resolve this problem, we propose a predictor-corrector technique. As the first step, we construct the volatility function as a constant. Then, in the next step, our algorithm follows the prediction step and correction step at half-backward time level. The constructed volatility function is continuous and piecewise linear with respect to the time variable. We demonstrate the ability of the proposed algorithm to reconstruct time-dependent volatility functions using manufactured volatility functions. We also present some numerical results for real market data using the proposed volatility function reconstruction algorithm.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 7026542
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3093708
OpenAlex ID: W2801890224
cites work: Stable local volatility function calibration using spline kernel
cites work: Pricing and hedging European-style options in Lévy-based stochastic volatility models considering the leverage effect
cites work: Accurate and efficient computations of the Greeks for options near expiry using the Black-Scholes equations
cites work: Efficient option pricing in crisis based on dynamic elasticity of variance model
cites work: Pricing collar options with stochastic volatility
cites work: The pricing of options and corporate liabilities
cites work: Recovery of time-dependent volatility in option pricing model
cites work: Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization
cites work: Using radial basis functions to construct local volatility surfaces
cites work: Calibration of the Local Volatility in a Generalized Black--Scholes Model Using Tikhonov Regularization
cites work: A robust and accurate finite difference method for a generalized Black-Scholes equation
cites work: From local volatility to local Lévy models
cites work: How to make Dupire’s local volatility work with jumps
Wikidata QID: Q129868635
Recommended article: Recovery of time-dependent volatility in option pricing model
Recommended article: Recovery of time-dependent parameters of a Black-Scholes-type equation: an inverse Stieltjes moment approach
Recommended article: Recovering the local volatility in Black–Scholes model by numerical differentiation
Recommended article: The Black-Scholes equation in stochastic volatility models
Recommended article: Q5143089
Recommended article: Fast reconstruction of time-dependent market volatility for European options
Recommended article: Reconstruction of local volatility for the binary option model
Recommended article: Recovery of the time-dependent implied volatility of time fractional Black-Scholes equation using linearization technique
Recommended article: Recovery of time dependent volatility coefficient by linearization
Recommended article: Reconstructing the unknown local volatility function
description: scientific article; zbMATH DE number 7026542