A nonparametric kernel regression approach for pricing options on stock market index

Previous options studies typically assume that the dynamics of the underlying asset price follow a geometric Brownian motion (GBM) when pricing options on stocks, stock indices, currencies or futures. However, there is mounting empirical evidence that the volatility of asset price or return is far from constant. This article, in contrast to studies that use parametric approach for option pricing, employs nonparametric kernel regression to deal with changing volatility and, accordingly, prices options on stock index. Specifically, we first estimate nonparametrically the volatility of asset return in the GBM based on the Nadaraya–Watson (N–W) kernel estimator. Then, based on the N–W estimates for the volatility, we use Monte Carlo simulation to compute option prices under different settings. Finally, we compare the index option prices under our nonparametric model with those under the Black–Scholes model and the Stein–Stein model.     

Foreign equity option pricing under stochastic volatility model with double jumps

This paper considers the challenging problem advocated by Huang and Hung (2005), that is to incorporate the stochastic volatility into the foreign equity option pricing. Foreign equity options (quanto options) are contingent claims where the payoff is determined by an equity in one currency but the actual payoff is done in another currency. Huang and Hung (2005) priced foreign equity options under the Lévy processes. In Huang and Hung's paper, they considered jumps in the foreign asset prices and exchange rates and assumed the volatility as constant. However, many studies showed that constant volatility and jumps in returns are incapable of fully capturing the empirical features of equity returns or option prices. In this paper, the stochastic volatility with simultaneous jumps in prices and volatility is proposed to model foreign asset prices and exchange rates. The foreign equity option pricing formula is given by using the Fourier inverse transformation. The numerical results show that the use of stochastic volatility with simultaneous jumps in prices and volatility proposed to model foreign asset prices and exchange rates is necessary and this approach can help us to capture more accurately the foreign equity option prices.     

On inferring standard deviations from path dependent options

Path dependent option prices are employed to derive implied standard deviations of the underlying security price process without recourse to numerical procedures. We empirically illustrate our methodology by inferring the volatility of gold prices.     

Modeling volatility and conditional correlations between socially responsible investments,gold and oil

Socially responsible investing (SRI) is one of the fastest growing areas of investing. While there is a considerable literature comparing SRI to various benchmarks, very little is known about the volatility dynamics of socially responsible investing. In this paper, multivariate GARCH models are used to model volatilities and conditional correlations between a stock price index comprised of socially responsible companies, oil prices, and gold prices. The dynamic conditional correlation model is found to fit the data the best and used to generate dynamic conditional correlations, hedge ratios and optimal portfolio weights. From a risk management perspective, SRI offers very similar results in terms of dynamic conditional correlations, hedge ratios, and optimal portfolio weights as investing in the S&P 500. For example, SRI investors can expect to pay a similar amount to hedge their investment with oil or gold as investors in the S&P 500 would pay. These results can help investors and portfolio managers make more informed investment decisions.     

Market depth,domestic investors and price monotonicity violations

We re-examine the monotonicity violations of option price dynamics considering the roles of market depth and domestic investors. Violations caused by option price movements in conflict with underlying price movements tend to occur less frequently as the market depth increases, especially in the case of out-of-the-money options. In contrast, violations caused by option prices that remain sticky despite underlying price changes occur more frequently as the market depth increases. Both of these relationships are amplified by domestic investors.     

Relationships among U.S. oil prices and oil industry equity indices

The cointegration analysis suggests that the pure oil industry equity system and the mixed oil price/equity index system offers more opportunities for long-run portfolio diversification and less market integration than the pure oil price systems. On a daily basis, in the oil price systems all oil prices with the exception of the 3-month futures can explain the future movements of each other. In the mixed system, none of the daily oil industry stock indices can explain the daily future movements of the New York Mercantile Exchange (NYMEX) futures prices, whereas these prices can explain the movements of independent companies engaged in exploration, refining, and marketing. The spillover analysis of oil volatility transmission suggests that the oil futures market has a matching or echoing volatility effect on the stocks of some oil sectors and a volatility-dampening effect on the stocks of others. The policy implication is that, during times of high oil volatility, traders should choose the S&P oil sector stocks that match their tolerance for volatility and use the right financial derivative to hedge against or profit from this volatility. The day effect for volatility transmission suggests that Friday has a calming effect on the volatility of oil stocks in general. The effect for Monday is not significant.     

Return and volatility transmission between world oil prices and stock markets of the GCC countries

This paper investigates the return links and volatility transmission between oil and stock markets in the Gulf Cooperation Council (GCC) countries over the period 2005-2010. We employ a recent generalized VAR-GARCH approach which allows for transmissions in return and volatility. In addition, we analyze the optimal weights and hedge ratios for oil-stock portfolio holdings. On the whole, our results point to the existence of substantial return and volatility spillovers between world oil prices and GCC stock markets, and appear to be crucial for international portfolio management in the presence of oil price risk.     

The forward pricing function of industrial metal futures – evidence from cointegration and smooth transition regression analysis

The prices of internationally traded metals have experienced wild swings and increased volatility in recent years. The relationship between spot and futures prices is an important topic in this context, as the current period’s price of a futures contract should be an unbiased estimator of next period’s spot price under the joint assumption of risk neutrality and rationality. Taking as a basis data from the Dow Jones UBS Commodity Index, which uses metals traded on the London Metal Exchange and US exchanges, this study adopts nonlinear smooth transition models to analyze whether the forward spread is a leading indicator of future spot price movements. Our findings suggest that such a price discovery function can in most cases only be identified in periods of low volatility or small previous spreads. Moreover, the underlying dynamics are captured best by the use of a logistic transition function.     

Nonlinear effects of oil shocks on stock returns: a Markov-switching approach

Using Markov-switching models, we investigate whether oil price shocks have nonlinear effects on stock returns. Empirical evidence from a set of international stock indexes suggests that an increase in oil prices has a negative and significant impact on stock prices in one state of the economy, whereas this effect is significantly dampened in another state of the economy. Furthermore, it is shown that changes in oil prices or in oil price volatility do not lead to a higher probability of switching between regimes.     

Asymmetric information in a competitive market game: Reexamining the implications of rational expectations

Summary. We examine price formation in a simple static model with asymmetric information, an infinite number of risk neutral traders and no noise traders. Here we re-examine four results associated with rational expectations models relating to the existence of fully revealing equilibrium prices, the advantage of becoming informed, the costly acquisition of information, and the impossibility of having equilibrium prices with higher volatility than the underlying fundamentals. Received: August 27, 1997; revised version: February 11, 1998     

A study of Shanghai fuel oil futures price volatility based on high frequency data: Long-range dependence,modeling and forecasting

In existing researches, the investigations of oil price volatility are always performed based on daily data and squared daily return is always taken as the proxy of actual volatility. However, it is widely accepted that the popular realized volatility (RV) based on high frequency data is a more robust measure of actual volatility than squared return. Due to this motivation, we investigate dynamics of daily volatility of Shanghai fuel oil futures prices employing 5-minute high frequency data. First, using a nonparametric method, we find that RV displays strong long-range dependence and recent financial crisis can cause a lower degree of long-range dependence. Second, we model daily volatility using RV models and GARCH-class models. Our results indicate that RV models for intraday data overwhelmingly outperform GARCH-class models for daily data in forecasting fuel oil price volatility, regardless the proxy of actual volatility. Finally, we investigate the major source of such volatile prices and found that trader activity has major contribution to fierce variations of fuel oil prices.     

Hedging and diversification across commodity assets

ABSTRACT

We investigate the conditional cross effects and volatility spillover between equity markets and commodity markets (oil and gold), Fama and French HML and SMB factors, volatility index (VIX) and bonds using different multivariate GARCH specifications considering the potential asymmetry and persistence behaviours. We analyse the dynamic conditional correlation between the US equity market and a set of commodity prices and risk factors to forecast the transmission of shock to the equity market firstly, and to determine and compare the optimal hedge ratios from the different models based on the hedging effectiveness of each model. Our findings suggest that all models confirm the significant returns and volatility spillovers. More importantly, we find that GO-GARCH is the best-fit model for modelling the joint dynamics of different financial variables. The results of the current study have implications for investors: (i) the equity market displays inverted dynamics with the volatility index suggesting strong evidence of diversification benefit; (ii) of the hedging assets gold appears the best hedge for the US equity market as it has a higher hedge effectiveness than oil and bonds over time; and (iii) despite these important results, a better hedge may be obtained by using well-selected firm sized and profitability-based portfolios.     

The limitation of monotonicity property of option prices: an empirical evidence

Many option pricing models are based on the assumption that the underlying asset price follows one-dimensional diffusion process. An alternative approach is to test the properties that should hold for all models based on a given stochastic process for the underlying asset. Following Pérignon (2006 Pérignon, C. 2006. Testing the monotonicity property of option prices. Journal of Derivatives, 14: 61–76. [Crossref] , [Google Scholar]), we test the empirical validity of the monotonicity property for option prices by collecting all transaction data from 1 July 2006 to 31 December 2006 for option contracts traded on the Taiwan Futures Exchange (TAIFEX). We find that sampled intraday option prices violate the monotonicity property between 29.97% and 57% of the time, and that call and put prices often increase, or decrease, together. We also find evidence to show that the frequent violations of the monotonicity property are to a large extent attributable to microstructure effects and that they arise from rational trading tactics.     

Psychology,Stock/FX Trading and Option Prices

The financial crisis of 2008 had many putative causes where psychology was an important driver for human decisions. However, quantitative financial models have no “knobs” to dial psychology parameters, and so arguably cannot possibly cope with financial crises. Here we take a first step by considering how a particular aspect of psychology can influence an underlying security and subsequent option prices, in a quantitative model. We investigate how psychological regret and fear impact trading selling behavior and induces changes in underlying security prices. We then consider the resulting changes in option prices with empirical evidence.     

The volatility of Australian traded goods’ prices

It is generally accepted that the Australian economy is continually subject to unanticipated shocks, particularly, unexpected swings in the prices of Australia's internationally- traded goods. This article empirically investigates the nature and extent of volatility in import and export prices faced by the Australian production sector. It estimates multivariate GARCH models of the stochastic processes generating the prices of imports and exports, and of important components of exports and imports. This article proposes an index of volatility, which is used to provide a summary measure of the extent of volatility in a multivariate context. The overall conclusion is that the price growth rates for Australia's traded goods exhibit considerable time variation in volatility and that these price growth rates are highly and positively correlated with each other.     

Accounting for the impact of higher order moments in foreign equity option pricing model

This paper investigates the pricing of foreign equity option whose value depends on foreign equity prices and exchange rate. We assume that the underlying asset returns of foreign equity option is not a Brownian motion, and use the Gram-Charlier series expansion to augment a normal density with two additional terms to capture the effects of skewness and kurtosis. The empirical study shows that the higher order moments (skewness and kurtosis) clearly affect the estimated prices of foreign equity options. This approach enables us to capture more accurately the foreign equity option prices.     

Regulatory Tools and Price Changes in Futures Markets

There is an extant literature investigating the relation between futures price limits and the volatility of futures price changes. An equally impressive number of papers investigates margin levels and their relation with price volatility. Very few papers explicitly model the indirect relation, through volatility, between margins and limits. Brennan's (1986) model is an exception. In his model, price limits help control contract default risk, thereby reducing required margins and ultimately lead to lower transaction costs. The crucial assumption in Brennan's model is the absence of accurate price signals when prices are locked at the limit. The paper extends Brennan's model with more realistic price change distributions that capture the typical characteristics of futures prices such as fat tails and time-varying volatility. It also discusses how learning can occur and how this may affect cost minimising optimality of regulation.     

An assessment of the empirical magnitude of option values for environment goods

This paper provides an empirical assessment of the magnitude of option values relative to expected surplus using a model presented by Larson and Flacco (1992). Option values and option prices are computed for both simulated data sets and actual estimates of recreation demands. Results indicate that option values engendered by price and income uncertainty are generally quite a small percent of expected surplus.     

Strategic use of futures and options by commodity processors

The impacts of input–output price relationships on end-users' demands for positions in futures and options are analyzed using a mean-variance portfolio model and applied to price risk management in the bread manufacturing industry. A production relationship was assumed between the input and resultant output, and correlation between the input and output prices were introduced into the portfolio model. The optimal hedge ratio can be either positive or negative depending upon the relationship between the input and output price standard deviation adjusted for production technology and input–output price correlation. Introduction of a call option into the portfolio (in addition to the futures) does not change the hedging demand for futures; however, the speculative component changes. The results show that the addition of input–output linear production and price correlation relationships would not justify a hedging role for options unless there is bias in the futures and/or options markets.     

期货市场与现货市场之间的价格研究--中国农产品市场的经验

本文借助于信息共享模型与波动溢出效应模型对我国大豆和小麦的期、现货市场之间的价格发现进行了多层次的实证研究,定量描述了期、现货市场在价格发现中作用的大小,深入刻画了我国农产品期、现货市场之间的动态关系.研究结果显示:大豆期、现货价格之间存在双向引导关系,小麦仅存在期货对现货的单向引导关系;期、现货市场均扮演着重要的价格发现角色,且期货市场在价格发现中处于主导地位;期、现货市场之间均存在双向波动溢出关系,但现货市场来自期货市场的波动溢出效应均强于期货市场来自现货市场的波动溢出效应;并且,随着期货市场的发展,期、现货市场之间的波动溢出程度均呈逐渐增强态势.