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

References

[1] Apaka,R.,Onyango,S.N., Omolo, O., Nyakinda,O.(2015). Modelling of Jumps and MeanReversion in Kenya Interest rates; International Journal of marketing and TechnologyVol. 5(11): pp. 8 – 11.

[2] Balvers.,Ronald., Wu., Yangru., Gilliland., Eric. (2000). Mean Reversion Across National Stock Markets and Parametric Contrarian Investment Strategies, The Journal of Finance, Vol. 2, 745-772.

[3] Bayraktar, E., Xing, H. (2010). Pricing Asian Options for jump Diffusion. The Journal of Mathematical Finance,Vol 49, 1467-9965.

[4] Black, F.,Scholes, N.(1973). The pricing options and corporate liabilities. Journal ofpolitical Economy Vol 18, 637-659.

[5] Cecchetti., Stephen., Pok-Sang., Lam., Nelson., Mark.(1990). Mean reversion in equilibrium asset prices, American Economic Review, 80, 398- 418.

[6] Chaudhuti., Kausik., Wu., Yangru.(2004). Mean Reversion in Stock Prices: Evidence from Emerging Markets, Managerial Finance, vol.30, 22-37.

[7] Cutler., David M., Poterba., JamesM., Summers., Lawrence, H. (1991). Speculative dynamics, Review of Economic Studies, 58, 529-546.

[8] DeBondt., Werner., Thaler., Richard.(1985). Does the Stock Market Overreact?, Journal of Finance,40, 793-805.

[9] Engel., Charles., Morris., Charles, S.(1991). Challenges to Stock Market Efficiency: Eviidence from Mean Reversion Studies, Economic Review.

[10] Fama., Eugene., French., Kenneth.(1988). Permanent and Temporary Components of Stock Prices, Journal of Political Economy, 96, 246-273.

[11] Huang,Z.,Kou,S.G.(2006).First passage times and analytical solutions for options on two assets with jump risk. Preprint, Columbia University.

[12] Hull, C. J.(2000).Options, Futures and other derivatives. Joseph L.Rotman School of Management, University of Toronto 4th Edition.

[13] Kim., Myung,J., Nelson., Charles R., Startz., Richard.(1991). Mean Reversion in Stock Prices A Reappraisal of the Empirical Evidence, Review of Economic Studies, 58, 151-528.

[14] Kou., Steven, G. (2002). A Jump-Di_usion Model for Option Pricing, Management Science Vol.48, No.8, pp. 1086-1101.

[15] Merton., Robert,C. (1975). Option Pricing When Underlying Stock Returns are Discontinuous. Masachusetts Institute of Technology.Vol.16, No.22, pp. 225-443.

[16] Nyakinda.,Otula,J.(2011). Derivation of Non-Linear Logistic Black-Scholes-Merton Partial Differential Equation; PhD Thesis, Jaramogi Oginga Odinga University of Science and Technology.

[17] Oduor, D. B., Omolo, O.N., Okelo, N. B,.Onyango, S. N. (2012). Estimation of Market Volatility: A case of logistic Brownian motion. International Journal of marketing and Technology Vol. 2(1): 32 - 48 2

[18] Oduor, D. B., Onyango, S.N. (2012). A logistic Brownian motion with a price of dividend yielding Asset. International Journal of Research and Social Sciences Vol. 2(2): 44 52.

[19] Onyango, S. N. (2003). Extracting Stochastic process from market price data: A pattern recognition approach. PhD Thesis (University of Huddersfield - UK)

[20] Samuelson, P. A. (1965). The stability of equilibrium.. Comparative Statistics and Dynamics,(Econometrics). Vol 9; 97-120.

[21] Verlhust, P. A.(1838). Notice on the law that the population follows in its increase. Mathematical and Physical Correspondence No 10; 113-121.2

@article{1702628,
      author = {Andanje Mulambula},
      title = {Estimation of Volatility Using European Logistic-Type Brownian motion When Asset Price Is Discontinuous},
      journal = {Iconic Research And Engineering Journals},
      year = {2021},
      volume = {4},
      number = {9},
      pages = {57-63},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1702628.pdf},
      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.},
      month = {March},
  }