scholarly journals Pricing of Two Kinds of Power Options under Fractional Brownian Motion, Stochastic Rate, and Jump-Diffusion Models

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Kaili Xiang ◽  
Yindong Zhang ◽  
Xiaotong Mao
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Financial Mathematics ◽  
Critical Issues ◽  
Option Pricing Model ◽  
Basic Hypothesis

Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. In this paper, under the assumption that the exchange rate follows the extended Vasicek model, we obtain the closed form of the pricing formulas for two kinds of power options under fractional Brownian Motion (FBM) jump-diffusion models.

scholarly journals Good Volatility, Bad Volatility, and Option Pricing

2018 ◽  
Vol 54 (2) ◽  
pp. 695-727 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Asset Price ◽  
Jump Diffusion ◽  
Quadratic Variation ◽  
Pricing Model ◽  
Economic Gain ◽  
Underlying Asset ◽  
Model Free ◽  
Option Pricing Model

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

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 On the Solution of Fractional Option Pricing Model by Convolution Theorem

2019 ◽  
pp. 143-157
Author(s):  
A. I. Chukwunezu ◽  
B. O. Osu ◽  
C. Olunkwa ◽  
C. N. Obi
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Hurst Exponent ◽  
Convolution Theorem ◽  
Pricing Model ◽  
One Dimensional ◽  
Black Scholes ◽  
Option Pricing Model

The classical Black-Scholes equation driven by Brownian motion has no memory, therefore it is proper to replace the Brownian motion with fractional Brownian motion (FBM) which has long-memory due to the presence of the Hurst exponent. In this paper, the option pricing equation modeled by fractional Brownian motion is obtained. It is further reduced to a one-dimensional heat equation using Fourier transform and then a solution is obtained by applying the convolution theorem.

scholarly journals A fuzzy jump-diffusion option pricing model based on Merton formula

2021 ◽  
Author(s):  
Satrajit Mandal ◽  
Sujoy Bhattacharya
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Search Algorithm ◽  
Option Price ◽  
Jump Diffusion ◽  
Call Option ◽  
Pricing Model ◽  
Model Based ◽  
Option Pricing Model ◽  
Jump Diffusion Model

Abstract This paper proposes a fuzzy jump-diffusion option pricing model based on Merton's normal jump-diffusion price dynamics. The logarithm of the stock price is assumed to be a Gaussian fuzzy number and the diffusion and jump parameters of the Merton model are assumed to be triangular fuzzy numbers to model the impreciseness which occur due to the variation in financial markets. Using these assumptions, a fuzzy formula for a European call option has been proposed. Given any value of the option price, its belief degree is obtained by using the bisection search algorithm. The fuzzy call option prices have been defuzzified and it has been found that the fuzzy jump-diffusion model outperforms Wu's fuzzy Black- Scholes model. This is one of the first studies where the impreciseness of the stock price and input parameters has been modelled taking into account occasional large jumps in stock price trajectory and thereby proposing a fuzzy option pricing model.

scholarly journals Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Di Pan ◽  
Shengwu Zhou ◽  
Yan Zhang ◽  
Miao Han
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Transaction Cost ◽  
Asian Option ◽  
Option Value ◽  
Cost Rate ◽  
Geometric Average ◽  
Option Pricing Model ◽  
Analytical Expressions

Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.

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