A Robust Derivation of the Black-Scholes Partial Differential Equation System without the Self-Financing Hypothesis
Jeong-Hoon Kim1, Graeme Wake2
1. Department of Mathematics, Yonsei University, Seoul, Republic of Korea.
2. Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand.
Abstract: Delta hedging is the core of the derivation of the well-known Black-Scholes formula for the price of European options. When Ito calculus is used faithfully without the self-financing hypothesis, the dependence of the delta on both time and the underlying asset price variables is induced and subsequently a consistent version of the Black-Scholes partial differential equation system is derived for the option price and the delta. This paper proposes the system as a possible starting point of a more robust study of mathematical option pricing.
Keywords: Black-Scholes partial differential equation, Ito calculus, Self-financing, No arbitrage, Option pricing.
Pages: 97 – 103 | Full PDF Paper