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Search Results: 1 - 10 of 36370 matches for " stochastic volatility model "
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The Stochastic Volatility Model, Regime Switching and Value-at-Risk (VaR) in International Equity Markets  [PDF]
Ata Assaf
Journal of Mathematical Finance (JMF) , 2017, DOI: 10.4236/jmf.2017.72026
Abstract: In this paper, we estimate two stochastic volatility models applied to international equity markets. The two models are the log-normal stochastic volatility (SV) model and the two-regime switching model. Then based on the one-day-ahead forecasted volatility from each model, we calculate the Value-at-Risk (VaR) in each market. The estimated VaR measures from the SV are higher than those obtained from the regime-switching model for all markets and over all horizons. The exception is the Japanese market, where the stochastic volatility model generates low VaR estimates. Comparing those estimates with the unconditional return distribution, the two models generate smaller VaR measures; an evidence of the two models capturing volatility changes in international equity markets. Finally, we backtest each model and find that the performance of both models is the worst for the Canadian stock market, while the regime switching model does poorly for Germany. The results have significant implications for risk management, trading and hedging activities as well as in the pricing of equity derivatives.
Stochastic Volatility Jump-Diffusion Model for Option Pricing  [PDF]
Nonthiya Makate, Pairote Sattayatham
Journal of Mathematical Finance (JMF) , 2011, DOI: 10.4236/jmf.2011.13012
Abstract: An alternative option pricing model is proposed, in which the asset prices follow the jump-diffusion model with square root stochastic volatility. The stochastic volatility follows the jump-diffusion with square root and mean reverting. We find a formulation for the European-style option in terms of characteristic functions of tail probabilities.
Modeling Exchange Rate Dynamics in Egypt: Observed and Unobserved Volatility  [PDF]
Dina Rofael, Rana Hosni
Modern Economy (ME) , 2015, DOI: 10.4236/me.2015.61006
Abstract: The underlying study focuses on estimating and forecasting the volatility of exchange rate in Egypt based on ARCH type models and the State Space (SS) models, namely; the Stochastic Volatility (SV) and the Time-Varying Parameter (TVP) models. Moreover, the paper tests the predictive power of the conducted models to come up with a powerful technique that gives the best forward-looking stance of the exchange rate. Empirically, the paper utilizes daily exchange rate data spanning from January 2003 till June 2013. Evidently, it is found that the exchange rate returns in Egypt suffer from the volatility clustering phenomenon and that there exists a time-varying variance in the exchange rate series that has to be appropriately dealt with, while modelling nominal exchange rates. Additionally, with regard to the link between the volatility occurring in the stock market in Egypt and the volatility of the exchange rate market, it is found that there is a risk mismatch between the two markets. Therefore, further research is recommended in the future to suggest other exogenous variables that can help in explaining the volatility in the exchange rate returns in Egypt.
Accurately Forecasting Model for the Stochastic Volatility Data in Tourism Demand  [PDF]
Ya-Ling Huang, Yen-Hsien Lee
Modern Economy (ME) , 2011, DOI: 10.4236/me.2011.25091
Abstract: This study attempts to enhance the effectiveness of stochastic volatility data. This work presents an empirical case involving the forecasting of tourism demand to demonstrate the efficacy of the accuracy forecasting model. Work combining the grey forecasting model (GM) and Fourier residual modification model to refine the forecasting effectiveness for the stochastic volatility data, which can estimate fluctuations in historical time series. This study makes the following contributions: 1) combining the grey forecasting and Fourier residual modification models to refine the forecasting effectiveness for the stochastic volatility data, 2) providing an effective method for forecasting the number of international visitors to Taiwan, 3) improving the accuracy of short-term forecasting in cases involving sample data with significant fluctuations.
Pricing Volatility Referenced Assets
Alan De Genaro Dario
Revista Brasileira de Finan?as , 2006,
Abstract: Volatility swaps are contingent claims on future realized volatility. Variance swaps are similar instruments on future realized variance, the square of future realized volatility. Unlike a plain vanilla option, whose volatility exposure is contaminated by its asset price dependence, volatility and variance swaps provide a pure exposure to volatility alone. This article discusses the risk-neutral valuation of volatility and variance swaps based on the framework outlined in the Heston (1993) stochastic volatility model. Additionally, the Heston (1993) model is calibrated for foreign currency options traded at BMF and its parameters are used to price swaps on volatility and variance of the BRL / USD exchange rate.
Optimal Investment Problem with Multiple Risky Assets under the Constant Elasticity of Variance (CEV) Model  [PDF]
Hui Zhao, Ximin Rong, Weiqin Ma, Bo Gao
Modern Economy (ME) , 2012, DOI: 10.4236/me.2012.36092
Abstract: This paper studies the optimal investment problem for utility maximization with multiple risky assets under the constant elasticity of variance (CEV) model. By applying stochastic optimal control approach and variable change technique, we derive explicit optimal strategy for an investor with logarithmic utility function. Finally, we analyze the properties of the optimal strategy and present a numerical example.
Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications  [PDF]
Oleksandr Zhylyevskyy
Theoretical Economics Letters (TEL) , 2012, DOI: 10.4236/tel.2012.24074
Abstract: The model of Bates specifies a rich, flexible structure of stock dynamics suitable for applications in finance and economics, including valuation of derivative securities. This paper analytically derives a closed-form expression for the joint conditional characteristic function of a stock’s log-price and squared volatility under the model dynamics. The use of the function, based on inverting it, is illustrated on examples of pricing European-, Bermudan-, and American-style options. The discussed approach for European-style derivatives improves on the option formula of Bates. The suggested approach for American-style derivatives, based on a compound-option technique, offers an alternative solution to existing finite-difference methods.
Pricing of foreign currency options in the Serbian market
Jankovi? Irena
Economic Annals , 2009, DOI: 10.2298/eka0980091j
Abstract: The main idea of this paper is to find the most suitable approach to the valuation of foreign currency options in the Serbian financial market. Volatility analysis included the application of the GARCH model which resulted in the marginal volatility measure, which was used in the pricing of basic foreign currency options in the local market. The analysis is completed with an overview of the implementation of FX derivatives in the Serbian financial market.
Heston Model Calibration in the Brazilian Foreign Exchange (FX) Options Market
Marcelo Nóbrega da Costa,Joe Akira Yoshino
Revista Brasileira de Finan?as , 2004,
Abstract: Despite the relatively recent advance in the derivative industry, the European FX option market uses simple models such as Black (1976) or Garman and Kohlhagen (1983). This widespread practice hides very important quantitative effects that could be better explored by using alternative pricing models such as the one that incorporates the stochastic volatility features. Understanding and calibrating this type of pricing model represents a challenge in the current state of art in financial engineering, specially in emerging markets that are characterized by strong volatilities, periodic changing regimes and in most case suffering of liquidity, specially during the crisis. In this sense, this paper shows how to implement the Hestons Model for the Brazilian FX option market. This approach uses the volatility matrix provided by a pool of domestic market players. Although the Hestons Model presents a formal analytical solution it does not require simulation-, the closed form solutions show a mathematical complexity. Thus, the main objective of this work is to implement this model in the Brazilian FX market.
Uncertain Volatility Derivative Model Based on the Polynomial Chaos  [PDF]
Stefanos Drakos
Journal of Mathematical Finance (JMF) , 2016, DOI: 10.4236/jmf.2016.61007

In the modern financial market the derivative pricing considers the use of historical or implied volatility which is actually the forward expectation of uncertainty. The common way of derivative pricing is to use the volatility as constant value in the well known Black Sholes equation. The aim of the current work was to develop a model where the uncertainty of volatility propagates to the derivative pricing and hedging according to the Black-Sholes PDE considering the volatility as stochastic process rather as a constant. A stochastic finite element method using generalized polynomial chaos was used to develop an algorithm of uncertainty propagation solving finally a deterministic problem for derivative pricing. The output of the method leads to derivative price distribution and the results of Monte Carlo Method for the derivative’s distribution were used as the exact solution against those rose from the new algorithm.

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