## Abstract

The Black-Scholes differential equations are extensively proposed in multi-asset option prices. Modelling of the Black-Scholes differential equation is generally completed by applying a ∆-hedging method, which could first-rate be accomplished on entire markets. Another technique, which is done in this work, is by first modelling multi-asset option prices in a backward stochastic differential equation. This study starts constructing a multi-asset portfolio which is written in BSDEs. The Feynman-Kac concept offers the relation between BSDEs and the Black-Scholes differential equations. Then we obtain a theorem which explains that the solution of BSDEs of multi-asset portfolios exists and is unique. It is also a solution to the Black-Scholes differential equations. Finally, in the last part of this work, we give some simulations of multi-asset option prices which are executed in a software.

Original language | English |
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Pages (from-to) | 135-146 |

Number of pages | 12 |

Journal | Nonlinear Dynamics and Systems Theory |

Volume | 24 |

Issue number | 2 |

Publication status | Published - 2024 |

## Keywords

- Black-Scholes differential equations
- Feynman-Kac theorem
- backward stochastic differential equations (BSDEs)
- multi-asset option
- partial differential equations (PDEs)