Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022)

<Previous Article In Volume
Next Article In Volume>

A Monte Carlo Simulation Scheme for Basket Options with Barriers

Authors
Ni Cao1, *, b, †, Hui Mai2, *,a, †, Shuining Zhang3, *, c, †
1Department of Mathematical Sciences, University of Liverpool, L69 7ZL, United Kingdom;
2Farmer School of Business, Miami University – Oxford, Ohio 45056, United States.
3Weatherhead School of Management, Case Western Reserve University, Ohio 44106 United States.
†

These authors contributed equally.

*Corresponding Author Email: amaih@miamioh.edu
Corresponding Authors
Ni Cao, Hui Mai, Shuining Zhang
Available Online 26 March 2022.
DOI
10.2991/aebmr.k.220307.485How to use a DOI?
Keywords
Basket option; Barrier option; Monte-Carlo simulation; Volatility
Abstract

In this paper we introduce simulation pricing of a sample barrier call option on a basket of stocks under the multivariate Black-Scholes-Merton scheme. Ten S&P 500 stocks from different industries were chosen to compose the basket, with the weights assigned to be the optimizer of the basket’s Sharpe ratio. Knock-in and knock-out barriers of the options were set to be monitored daily. For simulation the model assumed that the prices of underlying assets were lognormal and correlated with constant drift rates and volatilities. Historical estimations to volatilities and correlations were used, while EWMA model were employed to obtain more representative results. Cholesky decomposition was introduced to generate correlated random vector. Further, we conducted sensitivity analysis over barrier prices, strike prices, and volatilities through our Macro program. 3D diagrams were drawn to illustrate changes in price with respect to multi variables. We drew conclusion that the barrier calls proposed had varying sensitivity to strike price and barrier level under different volatilities. We also discovered that while most barrier options had positive Vegas, the Vega of a knock-out option might be negative when the volatility was relatively too high for its barrier price.

Copyright
© 2022 The Authors. Published by Atlantis Press International B.V.
Open Access
This is an open access article under the CC BY-NC license.

Download article (PDF)

<Previous Article In Volume
Next Article In Volume>
Volume Title
Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022)
Series
Advances in Economics, Business and Management Research
Publication Date
26 March 2022
ISBN
978-94-6239-554-1
ISSN
2352-5428
DOI
10.2991/aebmr.k.220307.485How to use a DOI?
Copyright
© 2022 The Authors. Published by Atlantis Press International B.V.
Open Access
This is an open access article under the CC BY-NC license.

Cite this article

risenwbib
TY  - CONF
AU  - Ni Cao
AU  - Hui Mai
AU  - Shuining Zhang
PY  - 2022
DA  - 2022/03/26
TI  - A Monte Carlo Simulation Scheme for Basket Options with Barriers
BT  - Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022)
PB  - Atlantis Press
SP  - 2975
EP  - 2983
SN  - 2352-5428
UR  - https://doi.org/10.2991/aebmr.k.220307.485
DO  - 10.2991/aebmr.k.220307.485
ID  - Cao2022
ER  -