A Monte Carlo Simulation Scheme for Basket Options with Barriers
These authors contributed equally.
- 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.
Cite this article
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 -