TY - JOUR

T1 - On a Neural Network to Extract Implied Information from American Options

AU - Liu, Shuaiqiang

AU - Leitao, Álvaro

AU - Borovykh, Anastasia

AU - Oosterlee, Cornelis W.

N1 - Funding Information:
We would also like to thank Dr.ir Lech Grzelak for valuable suggestions, as well as Dr. Damien Ackerer for fruitful discussions. The author S. Liu would like to thank the China Scholarship Council (CSC) for the financial support.
Publisher Copyright:
© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - Extracting implied information, like volatility and dividend, from observed option prices is a challenging task when dealing with American options, because of the complex-shaped early-exercise regions and the computational costs to solve the corresponding mathematical problem repeatedly. We will employ a data-driven machine learning approach to estimate the Black-Scholes implied volatility and the dividend yield for American options in a fast and robust way. To determine the implied volatility, the inverse function is approximated by an artificial neural network on the effective computational domain of interest, which decouples the offline (training) and online (prediction) stages and thus eliminates the need for an iterative process. In the case of an unknown dividend yield, we formulate the inverse problem as a calibration problem and determine simultaneously the implied volatility and dividend yield. For this, a generic and robust calibration framework, the Calibration Neural Network (CaNN), is introduced to estimate multiple parameters. It is shown that machine learning can be used as an efficient numerical technique to extract implied information from American options, particularly when considering multiple early-exercise regions due to negative interest rates.

AB - Extracting implied information, like volatility and dividend, from observed option prices is a challenging task when dealing with American options, because of the complex-shaped early-exercise regions and the computational costs to solve the corresponding mathematical problem repeatedly. We will employ a data-driven machine learning approach to estimate the Black-Scholes implied volatility and the dividend yield for American options in a fast and robust way. To determine the implied volatility, the inverse function is approximated by an artificial neural network on the effective computational domain of interest, which decouples the offline (training) and online (prediction) stages and thus eliminates the need for an iterative process. In the case of an unknown dividend yield, we formulate the inverse problem as a calibration problem and determine simultaneously the implied volatility and dividend yield. For this, a generic and robust calibration framework, the Calibration Neural Network (CaNN), is introduced to estimate multiple parameters. It is shown that machine learning can be used as an efficient numerical technique to extract implied information from American options, particularly when considering multiple early-exercise regions due to negative interest rates.

KW - American options

KW - computational finance

KW - implied volatility

KW - Machine learning

KW - negative interest rates

UR - http://www.scopus.com/inward/record.url?scp=85134601208&partnerID=8YFLogxK

U2 - 10.1080/1350486X.2022.2097099

DO - 10.1080/1350486X.2022.2097099

M3 - Article

AN - SCOPUS:85134601208

SN - 1350-486X

VL - 28

SP - 449

EP - 475

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

IS - 5

ER -