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Stochastic Volatility (stochastic + volatility)
Terms modified by Stochastic Volatility Selected AbstractsTesting Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest RatesINTERNATIONAL REVIEW OF FINANCE, Issue 3-4 2002George J. Jiang In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous-time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk-neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk-neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk-neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long-term options, random jump tends to price the short-term options better, and option pricing based on multiple risk-neutral distributions significantly outperforms that based on a single risk-neutral distribution. [source] Forecasting volatility by means of threshold modelsJOURNAL OF FORECASTING, Issue 5 2007M. Pilar Muñoz Abstract The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out-of-sample forecasting ability of the SETAR-Threshold GARCH (SETAR-TGARCH) and the SETAR-Threshold Stochastic Volatility (SETAR-THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ,true' underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR-THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves. Copyright © 2007 John Wiley & Sons, Ltd. [source] Stochastic Volatility in a Macro-Finance Model of the U.S. Term Structure of Interest Rates 1961,2004JOURNAL OF MONEY, CREDIT AND BANKING, Issue 6 2008PETER D. SPENCER affine term structure model; macro finance; unit root; stochastic volatility This paper generalizes the standard homoscedastic macro-finance model by allowing for stochastic volatility, using the "square root" specification of the mainstream finance literature. Empirically, this specification dominates the standard model because it is consistent with the square root volatility found in macroeconomic time series. Thus it establishes an important connection between the stochastic volatility of the mainstream finance model and macro-economic volatility of the Okun,Friedman type. This research opens the way to a richer specification of both macro-economic and term structure models, incorporating the best features of both macro-finance and mainstream finance models. [source] Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate DerivativesTHE JOURNAL OF FINANCE, Issue 1 2006HAITAO LI ABSTRACT Most existing dynamic term structure models assume that interest rate derivatives are redundant securities and can be perfectly hedged using solely bonds. We find that the quadratic term structure models have serious difficulties in hedging caps and cap straddles, even though they capture bond yields well. Furthermore, at-the-money straddle hedging errors are highly correlated with cap-implied volatilities and can explain a large fraction of hedging errors of all caps and straddles across moneyness and maturities. Our results strongly suggest the existence of systematic unspanned factors related to stochastic volatility in interest rate derivatives markets. [source] Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption MarketsTHE JOURNAL OF FINANCE, Issue 5 2003Rong Fan This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR-swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR-swap market. [source] Specification Analysis of Option Pricing Models Based on Time-Changed Lévy ProcessesTHE JOURNAL OF FINANCE, Issue 3 2004Jing-zhi Huang We analyze the specifications of option pricing models based on time-changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we need to incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component. [source] Transform Analysis and Asset Pricing for Affine Jump-diffusionsECONOMETRICA, Issue 6 2000Darrell Duffie In the setting of ,affine' jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ,smirks' of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing. [source] Backtesting Derivative Portfolios with Filtered Historical Simulation (FHS)EUROPEAN FINANCIAL MANAGEMENT, Issue 1 2002Giovanni Barone-Adesi Filtered historical simulation provides the general framework to our backtests of portfolios of derivative securities held by a large sample of financial institutions. We allow for stochastic volatility and exchange rates. Correlations are preserved implicitly by our simulation procedure. Options are repriced at each node. Overall results support the adequacy of our framework, but our VaR numbers are too high for swap portfolios at long horizons and too low for options and futures portfolios at short horizons. [source] Valuing executive stock options: performance hurdles, early exercise and stochastic volatilityACCOUNTING & FINANCE, Issue 3 2008Philip Brown G13 Abstract Accounting standards require companies to assess the fair value of any stock options granted to executives and employees. We develop a model for accurately valuing executive and employee stock options, focusing on performance hurdles, early exercise and uncertain volatility. We apply the model in two case studies and show that properly computed fair values can be significantly lower than traditional Black,Scholes values. We then explore the implications for pay-for-performance sensitivity and the design of effective share-based incentive schemes. We find that performance hurdles can require a much greater fraction of total compensation to be a fixed salary, if pre-existing incentive levels are to be maintained. [source] Testing Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest RatesINTERNATIONAL REVIEW OF FINANCE, Issue 3-4 2002George J. Jiang In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous-time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk-neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk-neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk-neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long-term options, random jump tends to price the short-term options better, and option pricing based on multiple risk-neutral distributions significantly outperforms that based on a single risk-neutral distribution. [source] How Persistent is Stock Return Volatility?JOURNAL OF BUSINESS FINANCE & ACCOUNTING, Issue 5-6 2007An Answer with Markov Regime Switching Stochastic Volatility Models Abstract:, We propose generalised stochastic volatility models with Markov regime changing state equations (SVMRS) to investigate the important properties of volatility in stock returns, specifically high persistence and smoothness. The model suggests that volatility is far less persistent and smooth than the conventional GARCH or stochastic volatility. Persistent short regimes are more likely to occur when volatility is low, while far less persistence is likely to be observed in high volatility regimes. Comparison with different classes of volatility supports the SVMRS as an appropriate proxy volatility measure. Our results indicate that volatility could be far more difficult to estimate and forecast than is generally believed. [source] Stochastic Volatility in a Macro-Finance Model of the U.S. Term Structure of Interest Rates 1961,2004JOURNAL OF MONEY, CREDIT AND BANKING, Issue 6 2008PETER D. SPENCER affine term structure model; macro finance; unit root; stochastic volatility This paper generalizes the standard homoscedastic macro-finance model by allowing for stochastic volatility, using the "square root" specification of the mainstream finance literature. Empirically, this specification dominates the standard model because it is consistent with the square root volatility found in macroeconomic time series. Thus it establishes an important connection between the stochastic volatility of the mainstream finance model and macro-economic volatility of the Okun,Friedman type. This research opens the way to a richer specification of both macro-economic and term structure models, incorporating the best features of both macro-finance and mainstream finance models. [source] Why Has U.S. Inflation Become Harder to Forecast?JOURNAL OF MONEY, CREDIT AND BANKING, Issue 2007JAMES H. STOCK Phillips curve; trend-cycle model; moving average; great moderation We examine whether the U.S. rate of price inflation has become harder to forecast and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trend-cycle model with stochastic volatility or, equivalently, an integrated moving average process with time-varying parameters. This model explains a variety of recent univariate inflation forecasting puzzles and begins to explain some multivariate inflation forecasting puzzles as well. [source] Stochastic Volatility Corrections for Interest Rate DerivativesMATHEMATICAL FINANCE, Issue 2 2004Peter Cotton We study simple models of short rates such as the Vasicek or CIR models, and compute corrections that come from the presence of fast mean-reverting stochastic volatility. We show how these small corrections can affect the shape of the term structure of interest rates giving a simple and efficient calibration tool. This is used to price other derivatives such as bond options. The analysis extends the asymptotic method developed for equity derivatives in Fouque, Papanicolaou, and Sircar (2000b). The assumptions and effectiveness of the theory are tested on yield curve data. [source] Forecasting volatility for options valuationOPEC ENERGY REVIEW, Issue 3 2006Mahdjouba Belaifa The petroleum sector plays a neuralgic role in the basement of world economies, and market actors (producers, intermediates, as well as consumers) are continuously subjected to the dynamics of unstable oil market. Huge amounts are being invested along the production chain to make one barrel of crude oil available to the end user. Adding to that are the effect of geopolitical dynamics as well as geological risks as expressed in terms of low chances of successful discoveries. In addition, fiscal regimes and regulations, technology and environmental concerns are also among some of the major factors that contribute to the substantial risk in the oil industry and render the market structure vulnerable to crises. The management of these vulnerabilities require modern tools to reduce risk to a certain level, which unfortunately is a non-zero value. The aim of this paper is, therefore, to provide a modern technique to capture the oil price stochastic volatility that can be implemented to value the exposure of an investor, a company, a corporate or a Government. The paper first analyses the regional dependence on oil prices, through a historical perspective and then looks at the evolution of pricing environment since the large price jumps of the 1970s. The main causes of oil prices volatility are treated in the third part of the paper. The rest of the article deals with volatility models and forecasts used in risk management, with an implication for pricing derivatives. [source] Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate DerivativesTHE JOURNAL OF FINANCE, Issue 1 2006HAITAO LI ABSTRACT Most existing dynamic term structure models assume that interest rate derivatives are redundant securities and can be perfectly hedged using solely bonds. We find that the quadratic term structure models have serious difficulties in hedging caps and cap straddles, even though they capture bond yields well. Furthermore, at-the-money straddle hedging errors are highly correlated with cap-implied volatilities and can explain a large fraction of hedging errors of all caps and straddles across moneyness and maturities. Our results strongly suggest the existence of systematic unspanned factors related to stochastic volatility in interest rate derivatives markets. [source] Specification Analysis of Option Pricing Models Based on Time-Changed Lévy ProcessesTHE JOURNAL OF FINANCE, Issue 3 2004Jing-zhi Huang We analyze the specifications of option pricing models based on time-changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we need to incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component. [source] Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption MarketsTHE JOURNAL OF FINANCE, Issue 5 2003Rong Fan This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR-swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR-swap market. [source] Event-Induced Volatility and Tests for Abnormal PerformanceTHE JOURNAL OF FINANCIAL RESEARCH, Issue 2 2003Robert Savickas Abstract I analyze a simple test statistic for mean abnormal returns in the presence of stochastic volatility during both event and nonevent windows and in the presence of event-induced variance increases. Unlike previous tests, the parametric test evaluated here does not require that the volatility effect of the event be the same across all securities. Simulations show that the test exhibits nontrivial gains in power over previously developed parametric and nonparametric tests, and the true null hypothesis is rejected at appropriate levels. [source] A generalization of Rubinstein's "Pay now, choose later"THE JOURNAL OF FUTURES MARKETS, Issue 5 2008Jia-Hau Guo This article provides quasi-analytic pricing formulae for forward-start options under stochastic volatility, double jumps, and stochastic interest rates. Our methodology is a generalization of the Rubinstein approach and can be applied to several existing option models. Properties of a forward-start option may be very different from those of a plain vanilla option because the entire uncertainty of evolution of its price is cut off by the strike price at the time of determination. For instance, in contrast to the plain vanilla option, the value of a forward-start option may not always increase as the maturity increases. It depends on the current term structure of interest rates. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:488,515, 2008 [source] Pricing American options on foreign currency with stochastic volatility, jumps, and stochastic interest ratesTHE JOURNAL OF FUTURES MARKETS, Issue 9 2007Jia-Hau Guo By applying the Heath,Jarrow,Morton (HJM) framework, an analytical approximation for pricing American options on foreign currency under stochastic volatility and double jump is derived. This approximation is also applied to other existing models for the purpose of comparison. There is evidence that such types of jumps can have a critical impact on earlyexercise premiums that will be significant for deep out-of-the-money options with short maturities. Moreover, the importance of the term structure of interest rates to early-exercise premiums is demonstrated as is the sensitivity of these premiums to correlation-related parameters. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:867,891, 2007 [source] Nonlinear asymmetric models of the short-term interest rateTHE JOURNAL OF FUTURES MARKETS, Issue 9 2006K. Ozgur DemirtasArticle first published online: 18 JUL 200 This study introduces a generalized discrete time framework to evaluate the empirical performance of a wide variety of well-known models in capturing the dynamic behavior of short-term interest rates. A new class of models that displays nonlinearity and asymmetry in the drift, and incorporates the level effect and stochastic volatility in the diffusion function is introduced in discrete time and tested against the popular diffusion, GARCH, and level-GARCH models. Based on the statistical test results, the existing models are strongly rejected in favor of the newly proposed models because of the nonlinear asymmetric drift of the short rate, and the presence of nonlinearity, GARCH, and level effects in its volatility. The empirical results indicate that the nonlinear asymmetric models are better than the existing models in forecasting the future level and volatility of interest rate changes. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:869,894, 2006 [source] Is it important to consider the jump component for pricing and hedging short-term options?THE JOURNAL OF FUTURES MARKETS, Issue 10 2005In Joon Kim The usefulness of the jump component for pricing and hedging short-term options is studied for the KOSPI (Korean Composite Stock Price Index) 200 Index options. It is found that jumps have only a marginal effect and stochastic volatility is of the most importance. There is evidence of jumps in the underlying index but no evidence of jumps in the corresponding index options. However, these results may not be valid for individual equity options. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:989,1009, 2005 [source] Valuing credit derivatives using Gaussian quadrature: A stochastic volatility frameworkTHE JOURNAL OF FUTURES MARKETS, Issue 1 2004Nabil Tahani This article proposes semi-closed-form solutions to value derivatives on mean reverting assets. A very general mean reverting process for the state variable and two stochastic volatility processes, the square-root process and the Ornstein-Uhlenbeck process, are considered. For both models, semi-closed-form solutions for characteristic functions are derived and then inverted using the Gauss-Laguerre quadrature rule to recover the cumulative probabilities. As benchmarks, European call options are valued within the following frameworks: Black and Scholes (1973) (represents constant volatility and no mean reversion), Longstaff and Schwartz (1995) (represents constant volatility and mean reversion), and Heston (1993) and Zhu (2000) (represent stochastic volatility and no mean reversion). These comparisons show that numerical prices converge rapidly to the exact price. When applied to the general models proposed (represent stochastic volatility and mean reversion), the Gauss-Laguerre rule proves very efficient and very accurate. As applications, pricing formulas for credit spread options, caps, floors, and swaps are derived. It also is shown that even weak mean reversion can have a major impact on option prices. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:3,35, 2004 [source] An examination of the effectiveness of static hedging in the presence of stochastic volatilityTHE JOURNAL OF FUTURES MARKETS, Issue 9 2003Jason Fink Toft and Xuan (1998) use simulation evidence to demonstrate that the static hedging method of Derman et al. (1995) performs inadequately when volatility is stochastic. Particularly, the greater the "volatility of volatility," the poorer the static hedge. This article presents an alternative static hedging methodology, denoted the generalized static hedge, that appears to perform more reliably. Specifically, the value, delta, and vega of the static hedges closely approximate those values of the barrier option being hedged. Further, simulation evidence indicates that when volatility of volatility is large, the standard deviation of simulated cash flows from the generalized static hedge position is less than the standard deviation of simulated cash flows from previously defined static hedge positions. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:859,890, 2003 [source] Options on bond futures: Isolating the risk premiumTHE JOURNAL OF FUTURES MARKETS, Issue 2 2003Robert G. Tompkins The introduction of unspanned sources of risk (and frictions) implies that option prices include a risk premium. Prima facie evidence of the existence of risk premia in option prices is contained in the implied volatility smile patterns reported in the literature. This article isolates the risk premium (defined as the simple difference between estimated and observed option prices) on options on U.K. Gilts, German Bunds, and U.S. Treasury bond futures using models that include price jumps and stochastic volatility. This study finds that single and multi-factor stochastic volatility models with jumps may explain the empirical regularities observed in bond futures. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:169,215, 2003 [source] Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utilityAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009Jinzhu Li Abstract In this paper, we assume that an investor can invest his/her wealth in a bond and a stock. In our wealth model, the stochastic interest rate is described by a Cox,Ingersoll,Ross (CIR) model, and the volatility of the stock is proportional to another CIR process. We obtain a closed-form expression of the optimal policy that maximizes a power utility. Moreover, a verification theorem without the usual Lipschitz assumptions is proved, and the relationships between the optimal policy and various parameters are given. Copyright © 2009 John Wiley & Sons, Ltd. [source] Generalized dynamic linear models for financial time seriesAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2001Patrizia Campagnoli Abstract In this paper we consider a class of conditionally Gaussian state-space models and discuss how they can provide a flexible and fairly simple tool for modelling financial time series, even in the presence of different components in the series, or of stochastic volatility. Estimation can be computed by recursive equations, which provide the optimal solution under rather mild assumptions. In more general models, the filter equations can still provide approximate solutions. We also discuss how some models traditionally employed for analysing financial time series can be regarded in the state-space framework. Finally, we illustrate the models in two examples to real data sets. Copyright © 2001 John Wiley & Sons, Ltd. [source] HEAVY-TAILED-DISTRIBUTED THRESHOLD STOCHASTIC VOLATILITY MODELS IN FINANCIAL TIME SERIESAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2008Cathy W. S. Chen Summary To capture mean and variance asymmetries and time-varying volatility in financial time series, we generalize the threshold stochastic volatility (THSV) model and incorporate a heavy-tailed error distribution. Unlike existing stochastic volatility models, this model simultaneously accounts for uncertainty in the unobserved threshold value and in the time-delay parameter. Self-exciting and exogenous threshold variables are considered to investigate the impact of a number of market news variables on volatility changes. Adopting a Bayesian approach, we use Markov chain Monte Carlo methods to estimate all unknown parameters and latent variables. A simulation experiment demonstrates good estimation performance for reasonable sample sizes. In a study of two international financial market indices, we consider two variants of the generalized THSV model, with US market news as the threshold variable. Finally, we compare models using Bayesian forecasting in a value-at-risk (VaR) study. The results show that our proposed model can generate more accurate VaR forecasts than can standard models. [source] | ||||||||||||||||||||||||||||