Search results for "implied volatility"
showing 10 items of 31 documents
European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs
2003
Abstract In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: we extend the framework developed by Davis et al. (SIAM J. Control Optim., 31 (1993) 470) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whalley and Wilmott (RISK 7 (1994) 82). We provide a simulation analysis in order …
A Multivariate Non-Gaussian Stochastic Volatility Model with Leverage for Energy Markets
2009
Spot prices in energy markets exhibit special features like price spikes, mean-reversion inverse, stochastic volatility, inverse leverage effect and co-integration between the different commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. Second order structure and stationary issues of the model are analysed. Moreover the implied multivariate forward model is derived. Due to the flexibility of the model stylized facts of the forward curve as contango, backwardation and humps are explained. Moreover, a transformed-based method to price options on the forward is described, where fast and precise algorithms for price computations ca…
Firm Size and Volatility Analysis in the Spanish Stock Market
2011
In this article, three strongly related questions are studied. First, volatility spillovers between large and small firms in the Spanish stock market are analyzed by using a conditional CAPM with an asymmetric multivariate GARCH-M covariance structure. Results show that there exist bidirectional volatility spillovers between both types of firms, especially after bad news. Second, the volatility feedback hypothesis explaining the volatility asymmetry feature is investigated. Results show significant evidence for this hypothesis. Finally, the study uncovers that conditional beta coefficient estimates within the used model are insensitive to sign and size asymmetries in the unexpected shock re…
Univariate and multivariate statistical aspects of equity volatility
2004
We discuss univariate and multivariate statistical properties of volatility time series of equities traded in a financial market. Specifically, (i) we introduce a two-region stochastic volatility model able to well describe the unconditional pdf of volatility in a wide range of values and (ii) we quantify the stability of the results of a correlation-based clustering procedure applied to synchronous time evolution of a set of volatility time series.
Option-Implied Volatility Spillovers between Risk Factors in FX Markets and States of the Global Economy
2016
This study employs option price data to back out the implied portfolio volatilities of the dollar and carry trade risk factors of the G-10 currencies. To investigate expected volatility spillover effects between risk factors in FX markets, we extend Grobys (2015) and Diebold and Yilmaz (2009) by constructing expected volatility spillover indices based upon the forecast-error variance decomposition of Vector-Autoregression models employing option-implied portfolio volatilities. Surprisingly, the dollar and carry trade risk factors that are orthogonal in the first moment exhibit strong stochastic interrelations in the second expected moment. Our findings indicate that expected high spillover …
Open and Closed Positions and Stock Index Futures Volatility
2011
In this paper we analyze the relationship between volatility in index futures markets and the number of open and closed positions. We observe that, although in general both positions are positively correlated with contemporaneous volatility, in the case of S&P 500, only the number of open positions has influence over the volatility. Additionally, we observe a stronger positive relationship on days characterized by extreme movements of these contracting movements dominating the market. Finally, our findings suggest that day-traders are not associated to an increment of volatility, whereas uninformed traders, both opening and closing their positions, have to do with it.
Proportional Small Sample Bias in Pricing Kernel Estimations
2014
Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In a first step, we analyze theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader of potential computational issues coupled with statistical techniques. In a second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kern…
Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets
2013
In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.
European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis
2015
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.
THE CARMA INTEREST RATE MODEL
2014
In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.