Jump Diffusion & Stochastic Volatility Models for Option Pricing (Application in Python & MATLAB)

سال انتشار: 1400
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 285

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شناسه ملی سند علمی:

JR_IJFMA-5-20_007

تاریخ نمایه سازی: 10 آذر 1400

چکیده مقاله:

The Black-Scholes model assumes that the price of the underlying asset follows a geometric Brownian motion. This assumption has two implications: first, log-returns over any horizon are normally distributed with constant volatility σ and the second, stock price evolution is continuous, therefore, there is no market gaps. These conditions are commonly violated in practice: empirical returns typically exhibit fatter tails than a normal distribution, volatility is not constant over time, and markets do sometimes gap. The existence of volatility skew will misprice options price. Derived from these flaws, a number of models have proposed. In this paper we will analyze, simulate and compare two most important models which have widespread using: jump diffusion model and stochastic volatility model. Each of the aforementioned models have programmed in MATLAB and Python, then their results have been compared together in order to provide a robust understanding of each of them. Our results show that in comparison to Black-Scholes model these two models yield better performance.

نویسندگان

Hamid Jamshidi

Master of Finance, Department of Finance and Accounting, Tehran Faculty of Petroleum, Petroleum University of Technology, Tehran, Iran

Ali mohammad ghanbari

Assistant Professor, Department of Finance and Accounting, Tehran Faculty of Petroleum, Petroleum University of Technology, Tehran, Iran