Stochastic Volatility Research Papers - Academia.edu (original) (raw)
This article presents a generic hybrid numerical method to price a wide range of options on one or several assets, as well as assets with stochastic drift or volatility. In particular for equity and interest rate hybrid with local... more
This article presents a generic hybrid numerical method to price a wide range of
options on one or several assets, as well as assets with stochastic drift or volatility. In particular
for equity and interest rate hybrid with local volatility.
- by Robert Jarrow
- •
- by Yannis Yatracos
- •
- Leverage
- by Arianna Mingone
- •
- Clearing
In a three-period¯nite competitive exchange economy with incomplete¯nancial markets and retrading, we study the possibility of controlling asset price volatility through¯nancial innovation. We¯rst give su±cient conditions on preferences... more
In a three-period¯nite competitive exchange economy with incomplete¯nancial markets and retrading, we study the possibility of controlling asset price volatility through¯nancial innovation. We¯rst give su±cient conditions on preferences and endowments implying that whatever is the innovation which completes markets, it also reduces volatility, typically in this class of economies. We also numerically examine some interesting examples. Then we show the generic existence, even outside this class, of¯nancial innovation which decreases equilibrium price volatility. The existence is obtained under conditions of su±cient market incompleteness. The¯nancial innovation may consist of an asset which is only traded at time zero, or retraded, and with payo®s only at the terminal date. The existence is shown to be robust in the asset payo® space.
- by Meili Kovalenko
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This study introduces the intraday implied volatility (IV) for pricing the Australian dollar (AUD) options. The IV is estimated using the at-the-money one-month, two-month, and three-month maturity AUD options traded in the opening,... more
This study introduces the intraday implied volatility (IV) for pricing the Australian dollar (AUD) options. The IV is estimated using the at-the-money one-month, two-month, and three-month maturity AUD options traded in the opening, midday, and closing period of a trading day. The Mincer-Zarnowitz regression test evaluates the predictive power of IV to forecast the foreign exchange volatility for the within-week, one-week, and one-month horizon. The mean absolute error, mean squared error, and root mean squared error measures are employed to assess the performance of IV in estimating the price of currency options for the within-week, one-week, and one-month horizon. This study reveals four critical findings. First, a three-month maturity IV does not contain vital information for pricing options. Second, IV incorporated information is not relevant to compute the value of options for a horizon of less than a week. Third, IV in the closing period of Monday or Tuesday subsumes most of t...
The forex exchange rate is the most volatile aspect in financial studies. This study uses a bayesian approach to estimate dynamic correlation multivariate stochastic volatility, a case of the Kenya stocks. Data was obtained from the... more
The forex exchange rate is the most volatile aspect in financial studies. This study uses a bayesian approach to estimate dynamic correlation multivariate stochastic volatility, a case of the Kenya stocks. Data was obtained from the Central Bank of Kenya website depicting the daily exchange rates for a period of 12 years (2003-2015). Multivariate Stochastic Volatility (MSV) model was fitted and its residuals exhibited volatility clustering hence the use Dynamic Correlation Multivariate Stochastic Volatility (DC-MSV) was applied to address these characteristics. Using Akaike Information Criterion (AIC) and Deviance Information Criterion (DIC) found that the returns are leptokurtic and have fat tails. The study estimated posterior parameters of the model by using of Markovian chain Monte Carlo (MCMC) iterations that worked well. Empirical results suggest that the best specifications are those that allow for time-varying correlation coefficients. The dynamic correlation multivariate st...
ABSTRACT. Empirical distributions in finance and economics might show heavy tails, volatility clustering, varying mean returns and multimodality as part of their features. However, most sta-tistical models available in the literature... more
ABSTRACT. Empirical distributions in finance and economics might show heavy tails, volatility clustering, varying mean returns and multimodality as part of their features. However, most sta-tistical models available in the literature assume some kind of parametric form ...
Time varying volatility is crucially important in many economic and financial areas. Investors in the stock markets are obviously interested in the volatility of stock prices. High volatility of return in financial market may discourage... more
Time varying volatility is crucially important in many economic and financial areas. Investors in the stock markets are obviously interested in the volatility of stock prices. High volatility of return in financial market may discourage investors to invest in stock market and hence greater uncertainty. So we need to estimate the appropriate volatility model to capture the volatility. This study applies five time series forecasting volatility models such as Random Walk (RW), Historical Average (HA), Moving Average (MA), Exponential Smoothing (ES), Autoregressive Process (AP) and Simple Regression (SR) respectively to four selected companies of DSE. Result shows that in all four companies RW model capture volatility quite well among other competing models. Keywords- Volatility, closing price, return, volatility models.
In this paper, the insurer and reinsurer's strategy and the reinsurer's surplus were studied in the presence of some random environmental noise on the risky asset under logarithm utility function. A portfolio with one risky and risk free... more
In this paper, the insurer and reinsurer's strategy and the reinsurer's surplus were studied in the presence of some random environmental noise on the risky asset under logarithm utility function. A portfolio with one risky and risk free asset was considered such that the risky asset follows the geometric Brownian motion (GBM). It was also assume that the claim process of the insurer is a stochastic differential equation, and the reinsurer can buy proportional reinsurance policy as a backup for their investment. The maximum principle theory and Ito's lemma were used to derive our optimization problem. The Legendre transformation and dual theory with variable separation technique were used to solve the optimization problem under logarithm utility to obtain the optimal reinsurer strategy (ORS), optimal reinsurer policy (ORP) and the reinsurer's surplus. More so, some numerical analyses were presented to discuss the effectof somesensitive parameters on the ORS and ORP. The ORS was observed to be a decreasing function of the instantaneous volatility, risk free interest rate but an increasing function of the appreciation rate of the of the risky asset. Furthermore, the relationship between the surplus process and time, risky asset and environmental noise was also given.
The research presented in this paper provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their... more
The research presented in this paper provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple nonlinear financial derivatives as vanilla European options are typically priced by means of Monte–Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility — a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models wit...
In this paper, we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alòs [(2012) A... more
In this paper, we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alòs [(2012) A decomposition formula for option prices in the Heston model and applications to option pricing approximation, Finance and Stochastics 16 (3), 403–422, doi: https://doi.org/10.1007/s00780-012-0177-0 ] for Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi: https://doi.org/10.1093/rfs/6.2.327 ] SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models — models utilizing a variance process postulated by Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, ...
Data for calibration and out-of-sample error testing of option pricing models are provided alongside data obtained from optimization procedures in "On calibration of stochastic and fractional stochastic volatility models" [1].... more
Data for calibration and out-of-sample error testing of option pricing models are provided alongside data obtained from optimization procedures in "On calibration of stochastic and fractional stochastic volatility models" [1]. Firstly we describe testing data sets, further calibration data obtained from combined optimizers is visually depicted - interactive 3d bar plots are provided. The data is suitable for a further comparison of other optimization routines and also to benchmark different pricing models.