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

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Guohe Deng
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Stock Price ◽  
Option Price ◽  
Put Options ◽  
Put Option ◽  
Mixed Fractional Brownian Motion ◽  
Short Interest

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.

OPTION PRICING FOR PROCESSES DRIVEN BY MIXED FRACTIONAL BROWNIAN MOTION WITH SUPERIMPOSED JUMPS

2015 ◽  
Vol 29 (4) ◽  
pp. 589-596 ◽  
Author(s):  
B.L.S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Option Price ◽  
Motion Model ◽  
Price Process ◽  
European Call Option ◽  
Mixed Fractional Brownian Motion ◽  
Special Cases ◽  
Brownian Motion Model

We propose a geometric mixed fractional Brownian motion model for the stock price process with possible jumps superimposed by an independent Poisson process. Option price of the European call option is computed for such a model. Some special cases are studied in detail.

Pricing of perpetual American put option with sub-mixed fractional Brownian motion

2019 ◽  
Vol 22 (4) ◽  
pp. 1145-1154
Author(s):  
Feng Xu ◽  
Shengwu Zhou
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Asset Price ◽  
Put Options ◽  
No Arbitrage ◽  
American Put Option ◽  
Put Option ◽  
American Put Options ◽  
Mixed Fractional Brownian Motion ◽  
American Put

Abstract The pricing problem of perpetual American put options is investigated when the underlying asset price follows a sub-mixed fractional Brownian motion process. First of all, the sub-mixed fractional Black-Scholes partial differential equation is established by using the delta hedging method and the principle of no arbitrage. Then, by solving the free boundary problem, we get the pricing formula of the perpetual American put option.

Time-changed generalized mixed fractional Brownian motion and application to arithmetic average Asian option pricing

2017 ◽  
Vol 6 (3) ◽  
pp. 85
Author(s):  
ömer önalan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Long Range Dependence ◽  
Price Process ◽  
Inverse Gamma ◽  
Proposed Model ◽  
Mixed Fractional Brownian Motion ◽  
Time Periods

In this paper we present a novel model to analyze the behavior of random asset price process under the assumption that the stock price pro-cess is governed by time-changed generalized mixed fractional Brownian motion with an inverse gamma subordinator. This model is con-structed by introducing random time changes into generalized mixed fractional Brownian motion process. In practice it has been observed that many different time series have long-range dependence property and constant time periods. Fractional Brownian motion provides a very general model for long-term dependent and anomalous diffusion regimes. Motivated by this facts in this paper we investigated the long-range dependence structure and trapping events (periods of prices stay motionless) of CSCO stock price return series. The constant time periods phenomena are modeled using an inverse gamma process as a subordinator. Proposed model include the jump behavior of price process because the gamma process is a pure jump Levy process and hence the subordinated process also has jumps so our model can be capture the random variations in volatility. To show the effectiveness of proposed model, we applied the model to calculate the price of an average arithmetic Asian call option that is written on Cisco stock. In this empirical study first the statistical properties of real financial time series is investigated and then the estimated model parameters from an observed data. The results of empirical study which is performed based on the real data indicated that the results of our model are more accuracy than the results based on traditional models.

scholarly journals The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Chao Wang ◽  
Shengwu Zhou ◽  
Jingyuan Yang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Jump Diffusion ◽  
Default Intensity ◽  
Stochastic Interest ◽  
Jump Diffusion Model ◽  
Vulnerable Option ◽  
Vulnerable Options

Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.

scholarly journals OPSI SAHAM PADA PASAR MODAL DI INDONESIA (STUDI PASAR OPSI SAAT PASAR OPSI MASIH BERLANGSUNG DI BURSA EFEK INDONESIA)

2019 ◽  
Vol 2 (2) ◽  
pp. 300
Author(s):  
Syanti Dewi ◽  
Ishak Ramli
Keyword(s):  
Interest Rate ◽  
Stock Prices ◽  
Stock Price ◽  
Stock Exchange ◽  
Option Price ◽  
Stock Option ◽  
Exchange Market ◽  
Strike Price ◽  
Option Trading ◽  
Put Option

Stock option exchange market is not working anymore in the Indonesian Stock Exchange, using the data option exchange market for the running period 2007-2008, we analyzed the effect of stock price, strike price, time to maturity, volatility and risk- free interest rate on the stock option’s price of listed stock call or put option trading at the Indonesian Stock Exchange during 2007-2008. The results found that the stock price, strike price, time to maturity, volatility and risk-free interest rate are positive significantly affecting the stock option price either the buying option price or the selling option price in Indonesia Stock Exchange 2007-2008 period. While there were no variables that significantly affected the call option during the periode 2007-2008, furthermore stock prices and strike prices significantly affected the put option prices. Time to maturity, Volatility, and risk free interest rate did not significantly affect the put option prices.That is why the stock option exchange market stop since the investor were not sure to the stock option price versus the risk of the volatility, time to maturity, and riskfree rate.

scholarly journals Pricing Vulnerable Options in a Mixed Fractional Brownian Motion with Jumps

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Panhong Cheng ◽  
Zhihong Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Firm Value ◽  
Stock Price ◽  
Pricing Model ◽  
Mixed Fractional Brownian Motion ◽  
Actuarial Approach ◽  
Basic Parameters ◽  
Vulnerable Options ◽  
Economic Analyses

A new framework for pricing European vulnerable options is developed in the case where the underlying stock price and firm value follow the mixed fractional Brownian motion with jumps, respectively. This research uses the actuarial approach to study the pricing problem of European vulnerable options. An analytic closed-form pricing formula for vulnerable options with jumps is obtained. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the paper. Finally, we compare and analyze the pricing results of different pricing models and discuss the influences of basic parameters on the pricing results of our proposed model by using numerical simulations, and the corresponding economic analyses about these influences are given.

European Option Pricing under Fractional Stochastic Interest Rate Model

2010 ◽  
Vol 171-172 ◽  
pp. 787-790
Author(s):  
Wen Li Huang ◽  
Gui Mei Liu ◽  
Sheng Hong Li ◽  
An Wang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Stochastic Interest Rate ◽  
European Option ◽  
European Option Pricing ◽  
Stochastic Interest ◽  
Pde Method ◽  
And Control

Under the assumption of stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with fractional stochastic interest rate. By choosing suitable Hurst index, we can calibrate the pricing model, so that the price can be used as the actual price of option and control the risk management

Pricing Geometric Asian Options under Mixed Fractional Brownian Motion Environment with Superimposed Jumps

2018 ◽  
Vol 70 (1) ◽  
pp. 1-6 ◽  
Author(s):  
B.L.S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Driving Force ◽  
Stock Price ◽  
Index Formula ◽  
Hurst Index ◽  
Asian Options ◽  
Price Process ◽  
Mixed Fractional Brownian Motion ◽  
Independent Poisson Process

It has been observed that the stock price process can be modelled with driving force as a mixed fractional Brownian motion (mfBm) with Hurst index [Formula: see text] whenever long-range dependence is possibly present. We propose a geometric mfBm model for the stock price process with possible jumps superimposed by an independent Poisson process.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

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