# An Unhedgeable Black–Scholes–Merton Implicit Option?

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## Abstract

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## 1. Introduction

## 2. Black–Scholes–Merton: The Classical Model

#### 2.1. The Case of Vanilla Options

#### 2.2. The Evolution of the Value of a Derivative

#### 2.3. Optimal Financial Strategy

## 3. Black–Scholes–Merton: An Implicit Assumption

#### 3.1. The Implicit Assumption

#### 3.2. Market Networks and Non-Contractual Exchange Behavior

## 4. Black–Scholes–Merton: Relaxing the Implicit Assumption

#### 4.1. Formalizing the Hedge Portfolio

#### 4.2. In Search of the Optimal Financial Strategy

#### 4.3. Hedging Impossibility

## 5. Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Pereira, A.M.; Tarter, M.S.
An Unhedgeable Black–Scholes–Merton Implicit Option? *Risks* **2022**, *10*, 134.
https://doi.org/10.3390/risks10070134

**AMA Style**

Pereira AM, Tarter MS.
An Unhedgeable Black–Scholes–Merton Implicit Option? *Risks*. 2022; 10(7):134.
https://doi.org/10.3390/risks10070134

**Chicago/Turabian Style**

Pereira, Alfredo M., and M. Sean Tarter.
2022. "An Unhedgeable Black–Scholes–Merton Implicit Option?" *Risks* 10, no. 7: 134.
https://doi.org/10.3390/risks10070134