scholarly journals Optimal Trade Execution under Jump Diffusion Process: A Mean-VaR Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Tianmin Zhou ◽  
Can Jia ◽  
Handong Li
Keyword(s):  
Brownian Motion ◽  
Heavy Tails ◽  
Simulation Analysis ◽  
Asset Price ◽  
Jump Diffusion ◽  
Uncertain Information ◽  
Return Distribution ◽  
Optimal Execution ◽  
Jump Diffusion Model ◽  
Optimal Execution Problem

In the classical optimal execution problem, the basic assumption of underlying asset price is Arithmetic Brownian Motion (ABM) or Geometric Brownian Motion (GBM). However, many empirical researches show that the return distribution of assets may have heavy tails than those of normal distribution. The uncertain information impact on financial market may be considered as one of the main reasons for heavy tails of return distribution. To introduce this information impact, our paper proposes a Jump Diffusion model for optimal execution problem. The jumps in our model are described by the compound Poisson process where random jump amplitude depicts the information impact on price process. In particular, the model is simple enough to derive closed-form strategies under risk neutral and Mean-VaR criterion. Simulation analysis of the model is also presented.

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 A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Elisa Alòs ◽  
Jorge A. León ◽  
Monique Pontier ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Time Behavior ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
White Type ◽  
Short Time

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms

2016 ◽  
Vol 28 (5) ◽  
pp. 789-826 ◽  
Author(s):  
T. RAY LI ◽  
MARIANITO R. RODRIGO
Keyword(s):  
Differential Equation ◽  
Option Pricing ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Underlying Asset ◽  
Mellin Transforms ◽  
Diffusion Dynamics ◽  
Double Exponential ◽  
Jump Diffusion Model

In this article, we use Mellin transforms to derive alternative results for option pricing and implied volatility estimation when the underlying asset price is governed by jump-diffusion dynamics. The current well known results are restrictive since the jump is assumed to follow a predetermined distribution (e.g., lognormal or double exponential). However, the results we present are general since we do not specify a particular jump-diffusion model within the derivations. In particular, we construct and derive an exact solution to the option pricing problem in a general jump-diffusion framework via Mellin transforms. This approach of Mellin transforms is further extended to derive a Dupire-like partial integro-differential equation, which ultimately yields an implied volatility estimator for assets subjected to instantaneous jumps in the price. Numerical simulations are provided to show the accuracy of the estimator.

Distribution of Discrete Time Delta-Hedging Error via a Recursive Relation

2016 ◽  
Vol 6 (3) ◽  
pp. 314-336 ◽  
Author(s):  
Minseok Park ◽  
Kyungsub Lee ◽  
Geon Ho Choe
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Jump Diffusion ◽  
Recursive Relation ◽  
Strike Price ◽  
Delta Hedging ◽  
Approximate Distribution ◽  
Jump Diffusion Model ◽  
Path Dependent

AbstractWe introduce a new method to compute the approximate distribution of the Delta-hedging error for a path-dependent option, and calculate its value over various strike prices via a recursive relation and numerical integration. Including geometric Brownian motion and Merton's jump diffusion model, we obtain the approximate distribution of the Delta-hedging error by differentiating its price with respect to the strike price. The distribution from Monte Carlo simulation is compared with that obtained by our method.

scholarly journals Analysing the Nepali Stock Market with Stochastic Models

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Karan Singh Thagunna ◽  
Radal M Lochowski
Keyword(s):  
Brownian Motion ◽  
Stock Market ◽  
Diffusion Model ◽  
Stock Prices ◽  
Jump Diffusion ◽  
Efficient Market Hypothesis ◽  
Geometric Brownian Motion ◽  
Brownian Motion Model ◽  
Jump Diffusion Model ◽  
Daily Returns

In this article we analyse the behaviour of the Nepali stock market and movements of stock prices of selected companies using (i) Efficient Market Hypothesis (EMH) (ii) geometric Brownian motion model (gBm) and (iii) Merton’s jump-diffusion model. Using the daily returns of the NEPSE index and the daily returns of stock prices of selected companies we estimate the geometric Brownian motion model and Merton’s jump-diffusion model. Further, we compare both models to identify the best fit for the Nepali stock market data. Keywords: Black-Scholes model, Efficient Market Hypothesis, geometric Brownian motion, Merton’s jump-diffusion Model, Variance Ratio Test

scholarly journals Prediksi harga saham PT. Astra agro lestari TBK dengan jump diffusion model

2017 ◽  
Vol 3 (1) ◽  
pp. 57 ◽  
Author(s):  
Di Asih I Maruddani ◽  
Trimono Trimono
Keyword(s):  
Brownian Motion ◽  
Diffusion Model ◽  
Jump Diffusion ◽  
Geometric Brownian Motion ◽  
Jump Diffusion Model

Saham merupakan salah satu emiten yang paling banyak diperjualbelikan di pasar modal. Harga saham dan perubahannya merupakan dua indikator yang sering dijadikan bahan pertimbangan oleh para calon investor sebelum memutuskan untuk membeli saham suatu perusahaan. Harga saham hampir selalu mengalami perubahan, dan sulit diperkirakan bagaimana keadaannya pada periode yang akan datang. Terdapat berbagai metode yang dapat digunakan untuk memperikirakan harga saham pada periode yang akan datang. Diantaranya adalah pemodelan dengan Geometric Brownian Motion (GBM) dan pemodelan dengan GeometricBrownian Motion (GBM) dengan Jump. Metode GBM dapat memperediksi harga saham dengan baik apabila data return saham periode sebelumnya berdistribusi normal. Sedangkan jika pada data return saham periode sebelumnya memenuhi asumsi normalitas dan ditemukan adanya lompatan, maka digunakan metode Jump Diffusion. Prediksi harga saham AALI untuk periode 03/01/2017 sampai dengan 12/05/2017 dengan GBM menghasilkan akurasi peramalan yang baik, dengan nilai MAPE sebesar 11,26%. Prediksi harga saham AALI untuk periode 03/01/2017 sampai dengan 12/05/2017 dengan metode Jump Diffuison menghasilkan akurasi peramalan yang sangat baik, dengan nilai MAPE sebesar 2,60%. Berdasarkan nilai MAPE, model Jump Diffusion memberikan hasil yang lebih baik daripada model GBM.

scholarly journals Pricing Vulnerable Option under Jump-Diffusion Model with Incomplete Information

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yang Jiahui ◽  
Zhou Shengwu ◽  
Zhou Haitao ◽  
Guo Kaiqiang
Keyword(s):  
Numerical Experiment ◽  
Incomplete Information ◽  
Diffusion Processes ◽  
Asset Price ◽  
Jump Diffusion ◽  
Jump Risk ◽  
Underlying Asset ◽  
Jump Diffusion Processes ◽  
Jump Diffusion Model ◽  
Vulnerable Option

In this paper, the closed-form pricing formula for the European vulnerable option with credit risk and jump risk under incomplete information was derived. Noise was introduced to the option writers assets while the underlying asset price and the value of corporation were assumed to follow the jump-diffusion processes. Finally the numerical experiment showed that jumps of underlying assets would increase the value of the option, but noise of corporation value was opposite.

scholarly journals Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Panhong Cheng ◽  
Zhihong Xu
Keyword(s):  
Firm Value ◽  
Asset Price ◽  
Jump Diffusion ◽  
Bifractional Brownian Motion ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Actuarial Approach ◽  
Jump Diffusion Model ◽  
Vulnerable Options ◽  
Klein Model

In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. By using the actuarial approach, analytic formulae for pricing the European vulnerable options are derived. The proposed pricing model contains many existing models such as Black–Scholes model (1973), Merton jump-diffusion model (1976), Klein model (1996), and Tian et al. model (2014).

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