Estimation of Volatility Using European Logistic-Type Brownian motion When Asset Price Is Discontinuous

• Author(s): Andanje Mulambula
• Paper ID: 1702628
• Page: 57-63
• Published Date: 19-03-2021
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 4 Issue 9 March-2021

Abstract

Volatility is a measure of how unsure we are about the future of asset price, hence its estimation is very important for implementation, valuation and derivative pricing of assets. Volatility forecast is crucial as it affects investment choice and is the key input to valuation of corporate and public liabilities. It gives the idea about the stability of stock prices. Relatively high volatility implies that the stock price varies continuously within relatively large interval. Volatility is the standard deviation of the continuously compounded rate of return of the stock, per year. Volatility forecast is also the most important parameter affecting prices of market-listed options of which trading volume increased in the last decade. Volatility of an asset as used by Black-Scholes model is assumed to be constant throughout the duration of the derivative. This study involves European logistic-type option pricing with jump diffusion. Using the knowledge of logistic Brownian motion with the aid of Dupire approach we develop a logistic Brownian motion with jump diffusion model for price process.

Keywords

Black-Scholes formula, Jump diffusion, Logistic Brownian motion, Volatility, Wiener process.

Citations

IRE Journals:
Andanje Mulambula "Estimation of Volatility Using European Logistic-Type Brownian motion When Asset Price Is Discontinuous" Iconic Research And Engineering Journals Volume 4 Issue 9 2021 Page 57-63

IEEE:
Andanje Mulambula "Estimation of Volatility Using European Logistic-Type Brownian motion When Asset Price Is Discontinuous" Iconic Research And Engineering Journals, 4(9)