Long memory and the relation between options and stock prices

Huang, Teng-Ching; Tu, Yu-Chen; Chou, Heng-Chih

doi:10.1016/j.frl.2014.11.005

Cited by 10 publications

(3 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The experimental investigation on financial time series demonstrates that the logarithmic returns of underlying assets exhibit features of nonnormal, self-similarity, heavy tails, longrange dependence, in both autocorrelations and cross-correlations, and volatility clustering in the real world [1][2][3][4][5][6][7][8]. Since the fractional Brownian motion has two properties of self-similarity and long-range dependence, thus it may be a useful tool to capture these phenomena from the financial assets.…”

Section: Introductionmentioning

confidence: 99%

The valuation of double barrier options under mixed fractional Brownian motion model with transaction costs

Rezaei

2023

Preprint

View full text Add to dashboard Cite

One of the phenomena observed in the real market is long-range dependence. Mixed fractional Brownian motion with Hurst parameter can be a suitable tool to capture it. The main objective of this work is to numerically evaluate the double barrier options base on the fractional Black-Scholes equation under mixed fractional Brownian motion model with transaction costs and time-dependent parameters in a discrete-time setting when the change in the option price with time follows a fractal transmission system. We solve the fractional Black-Scholes equation by using an implicit difference scheme. Also, we numerically investigate the influence of model parameters on the double barrier option price. Numerical results are presented to confirm the theoretical findings. Mathematics Subject Classification. 60G22, 91G20, 91B25.

show abstract

Section: Introductionmentioning

confidence: 99%

The valuation of double barrier options under mixed fractional Brownian motion model with transaction costs

Rezaei

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…where N is the number of shares for common stocks, M is the number of shares for outstanding warrants, and S is the value of the underlying asset at maturity T . Brownian motion, which enables arbitrage-free market has been employed as the stochastic model to simulate logarithmic returns, of which research by [2][3][4] demonstrated that the logarithmic return distribution has characteristics such as fat tails, volatility smile and long-range dependence. This encourages studies, such as the ones by [5][6][7][8] that modelled long-range dependency by characterising the distribution of the logarithmic returns with fractional Brownian motion (FBM).…”

Section: Introductionmentioning

confidence: 99%

Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion

Ibrahim¹,

Laham²

2022

Math. Model. Comput.

View full text Add to dashboard Cite

Mixed fractional Brownian motion (MFBM) is a linear combination of a Brownian motion and an independent fractional Brownian motion which may overcome the problem of arbitrage, while a jump process in time series is another problem to be address in modeling stock prices. This study models call warrants with MFBM and includes the jump process in its dynamics. The pricing formula for a warrant with mixed-fractional Brownian motion and jump, is obtained via quasi-conditional expectation and risk-neutral valuation.

show abstract

“…However, none of the above works takes account of selfsimilarity and long-range dependence. A large number of empirical studies have shown that the distributions of the logarithm returns of the financial assets generally exhibit features of self-similarity and long-range dependence with heavy tails and volatility clustering in the real world (e.g., see Lo [21], Willinger et al [22], Cont [23], Kang and Yoon [24], Kang et al [25], and Huang et al [26]). To incorporate this issue, the fractional Brownian motion (fBM) is introduced, which can capture the long-range dependence of the asset returns and produce burstiness in its sample path.…”

Section: Introductionmentioning

confidence: 99%

Pricing Catastrophe Equity Put Options in a Mixed Fractional Brownian Motion Environment

Deng

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper considers the pricing of the CatEPut option (catastrophe equity put option) in a mixed fractional model in which the stock price is governed by a mixed fractional Brownian motion (mfBM model), which manifests long-range correlation and fluctuations from the financial market. Using the conditional expectation and the change of measure technique, we obtain an analytical pricing formula for the CatEPut option when the short interest rate is a deterministic and time-dependent function. Furthermore, we also derive analytical pricing formulas for the catastrophe put option and the influence of the Hurst index when the short interest rate follows an extended Vasicek model governed by another mixed fractional Brownian motion so that the environment captures the long-range dependence of the short interest rate. Based on the numerical experiments, we analyze quantitatively the impacts of different parameters from the mfBM model on the option price and hedging parameters. Numerical results show that the mfBM model is more close to the realistic market environment, and the CatEPut option price is evaluated accurately.

show abstract

Long memory and the relation between options and stock prices

Cited by 10 publications

References 28 publications

The valuation of double barrier options under mixed fractional Brownian motion model with transaction costs

The valuation of double barrier options under mixed fractional Brownian motion model with transaction costs

Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion

Pricing Catastrophe Equity Put Options in a Mixed Fractional Brownian Motion Environment

Contact Info

Product

Resources

About