Investing money involves different levels of risks depending on the choice of the investment. In finance, an investor is faced with the problems of where and when to invest; ability to regularly and dynamically build his portfolio of investments; ability to find investment strategies that give profits with zero initial expenditures; proper risk management; option pricing; and many more. Delta-hedging, which involves trading financial instruments strategically, helps investors to eliminate or reduce risk associated with option trading. This can be achieved by continuous re-balancing the portfolio of the stock and option to always have after re-balancing, a total delta of zero. Practically, hedging is being done periodically. This work deals with the Delta-hedging of a European Call Options in Black-Scholes under the replicating portfolio strategy. This replicating portfolio contains stocks and money market accounts. We obtain the initial value required to build a trading strategy that produces exact payoff and has similar cash flow as that of the Call Option at any time which is the replicating portfolio. From there, we derive the delta of a European Call Option. The condition of the self-financing trading strategy is satisfied by the replicating strategy. Generally, the payoff from delta-hedging a European option depends on the stock path.
| Published in | Mathematics Letters (Volume 11, Issue 4) |
| DOI | 10.11648/j.ml.20251104.11 |
| Page(s) | 71-76 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Delta Hedging, European Call Options, Black-Scholes Model, Replicating Portfolio, Trading Strategy
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APA Style
Adindu-Dick, J. I. (2025). Delta-Hedging of a European Call Options in Black-Scholes Under the Replicating Portfolio Strategy. Mathematics Letters, 11(4), 71-76. https://doi.org/10.11648/j.ml.20251104.11
ACS Style
Adindu-Dick, J. I. Delta-Hedging of a European Call Options in Black-Scholes Under the Replicating Portfolio Strategy. Math. Lett. 2025, 11(4), 71-76. doi: 10.11648/j.ml.20251104.11
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Download@article{10.11648/j.ml.20251104.11,
author = {Joy Ijeoma Adindu-Dick},
title = {Delta-Hedging of a European Call Options in Black-Scholes Under the Replicating Portfolio Strategy},
journal = {Mathematics Letters},
volume = {11},
number = {4},
pages = {71-76},
doi = {10.11648/j.ml.20251104.11},
url = {https://doi.org/10.11648/j.ml.20251104.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20251104.11},
abstract = {Investing money involves different levels of risks depending on the choice of the investment. In finance, an investor is faced with the problems of where and when to invest; ability to regularly and dynamically build his portfolio of investments; ability to find investment strategies that give profits with zero initial expenditures; proper risk management; option pricing; and many more. Delta-hedging, which involves trading financial instruments strategically, helps investors to eliminate or reduce risk associated with option trading. This can be achieved by continuous re-balancing the portfolio of the stock and option to always have after re-balancing, a total delta of zero. Practically, hedging is being done periodically. This work deals with the Delta-hedging of a European Call Options in Black-Scholes under the replicating portfolio strategy. This replicating portfolio contains stocks and money market accounts. We obtain the initial value required to build a trading strategy that produces exact payoff and has similar cash flow as that of the Call Option at any time which is the replicating portfolio. From there, we derive the delta of a European Call Option. The condition of the self-financing trading strategy is satisfied by the replicating strategy. Generally, the payoff from delta-hedging a European option depends on the stock path.},
year = {2025}
}
TY - JOUR T1 - Delta-Hedging of a European Call Options in Black-Scholes Under the Replicating Portfolio Strategy AU - Joy Ijeoma Adindu-Dick Y1 - 2025/12/17 PY - 2025 N1 - https://doi.org/10.11648/j.ml.20251104.11 DO - 10.11648/j.ml.20251104.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 71 EP - 76 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20251104.11 AB - Investing money involves different levels of risks depending on the choice of the investment. In finance, an investor is faced with the problems of where and when to invest; ability to regularly and dynamically build his portfolio of investments; ability to find investment strategies that give profits with zero initial expenditures; proper risk management; option pricing; and many more. Delta-hedging, which involves trading financial instruments strategically, helps investors to eliminate or reduce risk associated with option trading. This can be achieved by continuous re-balancing the portfolio of the stock and option to always have after re-balancing, a total delta of zero. Practically, hedging is being done periodically. This work deals with the Delta-hedging of a European Call Options in Black-Scholes under the replicating portfolio strategy. This replicating portfolio contains stocks and money market accounts. We obtain the initial value required to build a trading strategy that produces exact payoff and has similar cash flow as that of the Call Option at any time which is the replicating portfolio. From there, we derive the delta of a European Call Option. The condition of the self-financing trading strategy is satisfied by the replicating strategy. Generally, the payoff from delta-hedging a European option depends on the stock path. VL - 11 IS - 4 ER -
Department of Mathematics, Imo State University, Owerri, Nigeria
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