The Black-Scholes equation is an application of the parabolic partial differential equation (PDE) equation that is simplified as: av 82 a²v at 2 as? Here, V = V (5, t), t is time, s is the market value of the asset being optioned, and 8 is the constant volatility of the asset. Derive the explicit finite difference parabolic equation for the Black-Scholes equation and explain the derivation steps.

The Black-Scholes equation is an application of the parabolic partial differential equation (PDE) equation that is simplified as: av 82 a²v at 2 as? Here, V = V (5, t), t is time, s is the market value of the asset being optioned, and 8 is the constant volatility of the asset. Derive the explicit finite difference parabolic equation for the Black-Scholes equation and explain the derivation steps.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

1.) The Black-Scholes equation is an application of the parabolic partial differential equation
(PDE) equation that is simplified as:
8² a²v
at
2 as?
Here, V = V (s, t), t is time, s is the market value of the asset being optioned, and 8 is the
constant volatility of the asset. Derive the explicit finite difference parabolic equation for the
Black-Scholes equation and explain the derivation steps.

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