Derivation of Black-Scholes Equation Using Itô's Lemma

Yıl 2021, Cilt: 3 Sayı: 1, 38 - 49, 15.06.2021

Brandon Washburn Mehmet Dik

https://doi.org/10.47086/pims.956201

Öz

The Black-Scholes Equation is arguably the most influential financial equation, as it is an effective example of how to eliminate risk from a financial portfolio by using a hedged position.
Hedged positions are used by many firms, mutual funds and finance companies to increase the value of financial assets over time.
The derivation of the Black-Scholes equation is often considered difficult to understand and overly complicated, when in reality most confusion arises from misunderstandings in notation or lack of intuition around the mathematical processes involved.
This paper aims to take a simple look at the derivation of the Black-Scholes equation as well as the reasoning behind it.

Anahtar Kelimeler

Stochastic, Black-Scholes Equation, Itô Calculus

Teşekkür

Thank you to Ben Stucky for advising me on this paper and Darah Chavey for leading my mathematics colloquium

Kaynakça

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