American stochastic volatility call option pricing: A lattice based approach

This study presents a new method of pricing options on assets with stochastic volatility that is lattice based, and can easily accommodate early exercise for American options. Unlike traditional lattice methods, recombination is not a problem in the new model, and it is easily adapted to alternative volatility processes. Approximations are developed for European C.E.V. calls and American stochastic volatility calls. The application of the pricing model to exchange traded calls is also illustrated using a sample of market prices. Modifying the model to price American puts is straightforward, and the approach can easily be extended to other non-recombining lattices.     

A new spread estimator

A cynosure of the academic literature relating to initial public offerings (IPOs) is the question of why they are “mispriced” so frequently. The large and growing literature addressing this question is evidence as to its intractability. This paper develops a theory of underwriters’ behavior suggesting that they will exploit their private information to minimize the bilateral risks to themselves of firm-commitment IPOs. That minimization may cause them to knowingly underprice the issue. The main result in this paper is based, in part, on the premise that the random character of the investors’ demand for shares in the secondary market, given the spread, is governed by an estimable conditional probability distribution. The underwriters exploit their private knowledge of that probability distribution to influence the number of shares in the offering in such a way as to minimize their expected loss function.     

A volatility smile-based uncertainty index

Annals of Finance - We propose a new uncertainty index based on the discrepancy of the smile of FX options. We show that our index spikes near turbulent periods, forecasts economic activity and its...     

Central limit theorem for the realized volatility based on tick time sampling

A central limit theorem for the realized volatility estimator of the integrated volatility based on a specific random sampling scheme is proved, where prices are sampled with every ‘continued price change’ in bid or ask quotation data. The estimator is shown to be robust to market microstructure noise induced by price discreteness and bid–ask spreads. More general sampling schemes also are treated in case that the price process is a diffusion.     

A bias in the volatility smile

We show that even if options traded with Black–Scholes–Merton pricing under a known and constant volatility, meaning essentially in perfect markets, one would still obtain smiles, skews, and smirks. We detect this problem by pricing options with a known volatility and reverse engineering to back into the implied volatility from the model price that was derived from the assumed volatility. The returned volatilities follow distinctive patterns resulting from algorithmic choices of the user and the quotation unit of the option. In particular, the common practice of penny pricing on option exchanges results in a significant loss of accuracy in implied volatility. For the most common scenarios faced in practice, the problem primarily exists in short-term options, but it manifests for virtually all cases of moneyness of at least 10 % and often 5 %. While it is theoretically possible to almost eliminate the problem, practical limitations in trading prevent any realistic chance of avoiding this error. It is even more difficult to identify and control the problem when smiles also arise from market imperfections, as is widely accepted. We empirically estimate a very conservative lower bound of the effect at about 16 % of the observed smile for 30-day options. Thus, we document a previously unknown phenomenon that a portion of the volatility smile is not of an economic nature. We provide some best-practice recommendations, including the explicit specification of the algorithmic choices and a warning against using off-the-shelf routines.     

The threshold effect in expected volatility: a model based on asymmetric information

This article develops theoretical insight into the thresholdeffect in expected volatility, which means that large shocksare less persistent in volatility than small shocks. The modeluses the Kyle-Admati-Pfleiderer setup with liquidity traders,informed traders, and a market maker. Information is modeledas a GARCH process. It is shown that the GARCH process for informationis transformed into a TARCH process (for 'threshold GARCH')for the market price changes. Working with information flowsallows one to derive implications for trading volume and marketliquidity which provide the basis for a more complete test ofthe model.     

Autoregressive stochastic volatility models with heavy-tailed distributions: A comparison with multifactor volatility models

This paper examines two asymmetric stochastic volatility models used to describe the heavy tails and volatility dependencies found in most financial returns. The first is the autoregressive stochastic volatility model with Student's t-distribution (ARSV-t), and the second is the multifactor stochastic volatility (MFSV) model. In order to estimate these models, the analysis employs the Monte Carlo likelihood (MCL) method proposed by Sandmann and Koopman [Sandmann, G., Koopman, S.J., 1998. Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of Econometrics 87, 271–301.]. To guarantee the positive definiteness of the sampling distribution of the MCL, the nearest covariance matrix in the Frobenius norm is used. The empirical results using returns on the S&P 500 Composite and Tokyo stock price indexes and the Japan–US exchange rate indicate that the ARSV-t model provides a better fit than the MFSV model on the basis of Akaike information criterion (AIC) and the Bayes information criterion (BIC).     

A PDE method for estimation of implied volatility

In this paper it is proved that the Black–Scholes implied volatility satisfies a second order non-linear partial differential equation. The obtained PDE is then used to construct an algorithm for fast and accurate polynomial approximation for Black–Scholes implied volatility that improves on the existing numerical schemes from literature, both in speed and parallelizability. We also show that the method is applicable to other problems, such as approximation of implied Bachelier volatility.     

A note on institutional hierarchy and volatility in financial markets

From a statistical point of view, the prevalence of non-Gaussian distributions in financial returns and their volatilities shows that the Central Limit Theorem (CLT) often does not apply in financial markets. In this article, we take the position that the independence assumption of the CLT is violated by herding tendencies among market participants, and investigate whether a generic probabilistic herding model can reproduce non-Gaussian statistics in systems with a large number of agents. It is well known that the presence of a herding mechanism in the model is not sufficient for non-Gaussian properties, which crucially depend on the details of the communication network among agents. The main contribution of this article is to show that certain hierarchical networks, which portray the institutional structure of fund investment, warrant non-Gaussian properties for any system size and even lead to an increase in system-wide volatility. Viewed from this perspective, the mere existence of financial institutions with socially interacting managers contributes considerably to financial volatility.     

Impact of idiosyncratic volatility on stock returns: A cross-sectional study

This paper proposes a new approach to estimate the idiosyncratic volatility premium. In contrast to the popular two-pass regression method, this approach relies on a novel GMM-type estimation procedure that uses only a single cross-section of return observations to obtain consistent estimates. Also, it enables a comparison of idiosyncratic volatility premia estimated using stock returns with different holding periods. The approach is empirically illustrated by applying it to daily, weekly, monthly, quarterly, and annual US stock return data over the course of 2000–2011. The results suggest that the idiosyncratic volatility premium tends to be positive on daily return data, but negative on monthly, quarterly, and annual data. They also indicate the presence of a January effect.     

A generalized volatility bound for dynamic economies

We develop a generalization of the Hansen-Jagannathan (1991) volatility bound that (i) incorporates the serial correlation properties of return data and (ii) allows us to calculate a spectral version of the bound. This generalization enables us to judge whether models match important aspects of the data in the long run, at business cycle frequencies, seasonal frequencies, etc. Our bound permits evaluation of models without requiring their explicit solution in a way that respects the dynamic implications of the fundamental component of the models, namely, the Euler equation that links asset returns to the intertemporal marginal rate of substitution.     

Macroeconomic determinants of stock volatility and volatility premiums

How does stock market volatility relate to the business cycle? We develop, and estimate, a no-arbitrage model, and find that (i) the level and fluctuations of stock volatility are largely explained by business cycle factors and (ii) some unobserved factor contributes to nearly 20% to the overall variation in volatility, although not to its ups and downs. Instead, this “volatility of volatility” relates to the business cycle. Finally, volatility risk-premiums are strongly countercyclical, even more than stock volatility, and partially explain the large swings of the VIX index during the 2007–2009 subprime crisis, which our model captures in out-of-sample experiments.     

Local volatility of volatility for the VIX market

Following a trend of sustained and accelerated growth, the VIX futures and options market has become a closely followed, active and liquid market. The standard stochastic volatility models—which focus on the modeling of instantaneous variance—are unable to fit the entire term structure of VIX futures as well as the entire VIX options surface. In contrast, we propose to model directly the VIX index, in a mean-reverting local volatility-of-volatility model, which will provide a global fit to the VIX market. We then show how to construct the local volatility-of-volatility surface by adapting the ideas in Carr (Local variance gamma. Bloomberg Quant Research, New York, 2008) and Andreasen and Huge (Risk Mag 76–79, 2011) to a mean-reverting process.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

A four-factor stochastic volatility model of commodity prices

The number of factors driving the uncertain dynamics of commodity prices has been a central consideration in financial literature. While the majority of empirical studies relies on the assumption that up to three factors are sufficient to explain all relevant uncertainty inherent in commodity spot, futures, and option prices, evidence from Trolle and Schwartz (Rev Financ Stud 22(11):4423–4461, 2009b) and Hughen (J Futures Mark 30(2):101–133, 2010) indicates a need for additional risk factors. In this article, we propose a four-factor maximal affine stochastic volatility model that allows for three independent sources of risk in the futures term structure and an additional, potentially unspanned stochastic volatility process. The model principally integrates the insights from Hughen (2010) and Tang (Quant Finance 12(5):781–790, 2012) and nests many well-known models in the literature. It can account for several stylized facts associated with commodity dynamics such as mean reversion to a stochastic level, stochastic volatility in the convenience yield, a time-varying correlation structure, and time-varying risk-premia. In-sample and out-of-sample tests indicate a superior model fit to futures and options data as well as lower hedging errors compared to three-factor benchmark models. The results also indicate that three factors are not sufficient to model the joint dynamics of futures and option prices accurately.     

关于Shibor利率期权波动率定价机制的研究

Shibor自2007年发布以来,已成为人民币利率市场的一个重要定价基准,对金融衍生品、债券的定价起着十分重要的作用,由于人民币利率衍生品市场尚处于发展的初期,与美元Libor利率期权等较为成熟市场相比,目前Shibor利率期权缺少成熟的市场报价。本文通过风险中性的定价方程反解参数的方法,利用Shibor利率掉期曲线对Shibor利率上下限期权的隐含波动率进行计算,从而探讨对Shibor利率期权的定价。     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

The effects of Federal funds rate surprises on S&P 500 volatility and volatility risk premium

In this paper, we examine the effects of expected and surprise components in Federal funds target rate changes on realized and implied volatility. We find that surprise changes in the target rate significantly increase volatility. Consistent with the efficient market hypothesis, our analysis suggests that the expected component of a target rate change as well as the target rate change itself, do not significantly affect volatility. We also show that larger than expected decreases in the Federal funds target rate tend to lower the volatility risk premium.     

A multivariate nonparametric test for return and volatility timing

This paper develops a novel approach to simultaneously test for market timing in stock index returns and volatility. The tests are based on the estimation of a system of regression equations with indicator variables and provide detailed information about the statistical significance of alternative market timing components.     

The effects of trading activity on market volatility

The paper re-examines the question of excessive implied persistence of volatility estimates when GARCH type models are used. Ten actively traded US stocks are considered and as already established in the literature, when volume traded is inserted in the GARCH (1, 1) or (EGARCH 1, 1) models for returns, the estimated persistence is decreased. Since volume is affected also by within-the-day price movements and hence is not weakly exogenous relative to returns, alternative proxies for trading activities are suggested. It is concluded that the difference between the opening price and the closing price of the previous day accounts also for most of the persistence in the autoregressive conditional heteroskedasticity.