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.     

Is USD-INR Really an Excessively Volatile Currency Pair?

The USD-INR currency pair has often been in the news for its excess volatility. This study examines the veracity of this belief by using the extreme value estimator proposed by Rogers and Satchell (Ann Appl Prob 1(4):504–512, 1991) and the VRatio proposed by Maheswaran et al. (J Emerg Mark Finance 10(2):175–196, 2011). The volatility in the USD-INR exchange rate is determined for the period beginning January 2009 and ending June 2015. The volatility of the GBP-INR and EUR-INR currency pairs is also determined for making comparisons. The results show that the EUR-INR and the GBP-INR currency pairs exhibit excess volatility, but not the USD-INR. This result runs counter to the commonly held view. This study also examines the volatility of the three currency pairs using the multiple-days’ time windows for better approximation of Brownian motion while embedding the jumps in the daily opening prices. There is no evidence to support the existence of excess volatility in the USD-INR.

     

Analysis of High Frequency Data in Finance: A Survey

This study examines the use of high frequency data in finance, including volatility estimation and jump tests. High frequency data allows the construction of model-free volatility measures for asset returns. Realized variance is a consistent estimator of quadratic variation under mild regularity conditions. Other variation concepts, such as power variation and bipower variation, are useful and important for analyzing high frequency data when jumps are present. High frequency data can also be used to test jumps in asset prices. We discuss three jump tests: bipower variation test, power variation test, and variance swap test in this study. The presence of market microstructure noise complicates the analysis of high frequency data. The survey introduces several robust methods of volatility estimation and jump tests in the presence of market microstructure noise. Finally, some applications of jump tests in asset pricing are discussed in this article.     

Fiscal policy and asset price volatility

This paper investigates the relationship between volatility of different asset prices and the volatility of various indicators of fiscal policy (primary balance, spending and revenue). We find evidence that asset price volatility affects the volatility of fiscal policy stance in a positive and significant way. The effect comes primarily through residential property and equity price volatility on government revenue and spending. Increased volatility in commercial property prices is associated with increased variability of government revenue. Output growth volatility is the dominant determinant of revenue and primary balance variability, whereas bad budgetary conditions and the size of the public sector are the most significant determinants of spending variability. Trade openness leads to greater variability of government spending, revenue and primary balance to GDP ratios.     

Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method

The purpose of this paper is to consider the optimal proportional reinsurance and investment strategies for an insurance company. The insurer’s surplus process is approximated by a Brownian motion with drift. The insurance company can purchase proportional reinsurance and invest the surplus in a financial market which includes one risk-free asset and one risky asset whose price is modeled by a CEV model. The primary problem is changed to the dual problem by implying Legendre transform. When the objective of the insurance company is to maximize the expected logarithmic utility from terminal wealth, the closed-form expressions for the optimal reinsurance-investment policy which is different to the Merton case to the primal optimal problem are obtained and numerical simulations are provided to demonstrate our results. Moreover, we find an interesting result that risk exposure is non-monotonic in the cost of reinsurance.

     

The effect of FOMC statements on asset prices

Given their increased importance during recent years, FOMC (Federal Open Market Committee) statements can have a significant impact on asset prices. To capture the effect of FOMC statements on asset prices, an indicator variable is created that takes into account the information content of policy statements. Results show that both ‘interest rate surprises’ and ‘FOMC statements’ affect the mean and the volatility of asset prices. The volatility impact is tent-shaped, jumping within the policy announcement interval and declining before and after the release. FOMC statements have a much more pronounced impact on stock returns, intermediate and long-term yields, while short-term rates are largely driven by target rate decisions. We also find that the evolution of the language of the FOMC statements does matter to market participants and, in particular, the ‘forward-looking’ language adopted in mid-2003 has reduced market volatility associated with ‘interest rate surprises’ on announcement days.     

OPTIMAL MONETARY POLICY AND ASSET PRICE MISALIGNMENTS

This paper analyses the relationship between monetary policy and asset prices in the context of optimal policy rules. The transmission mechanism is represented by a linearized rational expectations model augmented for the effect of asset prices on aggregate demand. Stabilization objectives are represented by a discounted quadratic loss function penalizing inflation and output gap volatility. Asset prices are allowed to deviate from their intrinsic value due to momentum trading. We find that in the presence of wealth effects and inefficient markets, asset price misalignments from their fundamentals should be included in the optimal interest rate reaction function.     

马尔可夫调制模型下交换期权的定价

在这篇文章中,假定市场经济状态由一个两状态马尔可夫链描述,风险资产满足一个两状态的马尔可夫调制过程。当市场处于高波动状态时,风险资产的价格满足跳扩散过程;当市场处于稳定状态时,风险资产的价格满足几何布朗运动.通过测度变换的技术,得到了交换期权的定价公式。最后,利用蒙特卡洛方法给出了期权价值的数值结果。     

Asset prices and economic fluctuations: The implications of stochastic volatility

This paper investigates whether the multi-factor stochastic volatility of stock returns is related to economic fluctuations and affects asset prices. We address these issues in a dynamic Fama-French three-factor volatility model framework. Consistent with the ICAPM with stochastic volatility (Campbell et al., 2017), we find that the conditional volatility of the size and value factors is significantly related to economic uncertainty. These volatilities are also significant pricing factors. The out-of-sample forecasting analysis further reveals that the conditional volatility can predict stock returns and deliver economic gain in asset allocation. Our analysis sharpens the understanding on the link between the stock market and economic fundamentals.     

Discontinuities in the coal market

Coal has been an important source of energy in the USA for centuries. Coal prices can be quite uncertain and highly volatile, often experiencing large changes. Understanding the data-generating process of coal prices would seem critical, both from a market perspective and from a policy perspective. This study investigates the appropriate stochastic process underlying coal prices. Commonly assumed processes, such as geometric Brownian motion fail to properly account for the arrival of unanticipated information which inflicts rapid changes – or jumps – in energy markets. Such discontinuities can manifest ‘fat tails’ in the distribution of returns. To investigate the possibility of time-varying volatility, generalized autoregressive conditional heteroscedastic models are also incorporated into the analysis. We find compelling empirical evidence that discontinuities must not be ignored, with US coal prices experiencing jumps every few days. The result has implications for the potential closure of coal-fired plants in response to cheaper alternatives or climate-based regulations.     

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.     

Determinants of stock price bubbles

In this paper we propose a cross-sectional model of the determinants of asset price bubbles. Using 589 firms listed on the NYSE, we find conclusive evidence that trading volume and share price volatility have statistically significant effects on asset price bubbles. However, evidence from sector-based stocks is mixed. We find that for firms belonging to electricity, energy, financial, and banking sectors, and for the smallest size firms, trading volume has a statistically significant and positive effect on bubbles. We do not discover any robust evidence of a statistically significant effect of share price volatility on bubbles at the sector-level.     

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.     

On the Effects of Asset Purchase Programs on Emerging Stock Markets

ABSTRACT

It is well documented that there has been a relationship between stock markets and unconventional monetary policies. However, most research concentrates on developed economies and analyzes the effects of shocks from such polices on stock prices. This paper is different from this research in that we investigate the impact of surprises from the Fed’s and the ECB’s announcements on the stock returns and volatility in Gulf Cooperation Council (GCC) countries using GARCH models. We find that a positive surprise associated with a fall in the U.S. Treasury yield causes an increase in ADX returns. We show significant effects of the ECB’s shocks on price returns. In particular, announcement that induces a decline in yield spreads in Italian sovereign bonds leads to higher stock prices. We also document a significant impact of surprises both by the Fed and ECB on volatility. However, the estimates are mixed. We note that volatility went down in response to the ECB’s policies, while they increased after the Fed’s asset purchases. Finally, when we distinguish surprises by their sign, the GJR-GARCH model estimates indicate that the effect on the volatility which is, perhaps surprisingly, symmetric for both types of news.     

On the usefulness of intraday price ranges to gauge liquidity in cap-based portfolios

We find that easy-to-observe price ranges are useful for estimating intraday liquidity. Following the literature on range-based volatility estimators, we go beyond the use of the closing price only and rely on the full range of prices. Based on high, low, opening, and closing (HLOC) prices, we show that a greater intensity in the price discovery process (as measured by the open–close range) and a higher level of price uncertainty (as captured by the High–Low range) lower ex-ante liquidity for small, mid, and large caps. Realized volatility (RV) fails to capture these effects. Although order books have become increasingly difficult to treat, there is some good news: it has never been easier to look at price ranges.     

International asset prices and portfolio choices under Bayesian learning

We calculate equilibrium asset prices and portfolio choices from a two-country OLG international asset pricing model under the assumption that investors are on a Bayesian learning path. Investors from both countries receive identical information flows, but domestic investors start off with less precise priors concerning foreign fundamentals. Learning is shown to produce first-order effects on the properties of asset prices, in the form of increased equity returns, volatility clustering, and time-varying correlations across national stock markets. Moreover, on a learning path, estimation risk generates portfolio biases similar to those observed empirically, i.e. a strong preference towards domestic securities and excessive turnover in foreign securities. These findings are robust to changes in prior beliefs, the calibration of initial information asymmetries, and the parameterization of the model. We use real GDP data for the US and Europe to calibrate the model and show that in the event of a financial liberalization during the 1970s, high excess returns, time-varying volatility, substantial home bias, and excess turnover should have been observed.     

Two-period trading sentiment asset pricing model with information

We present a dynamic asset pricing model with investor sentiment and information, which shows that the investor sentiment plays a systematic and important role in the asset prices and the information is gradually incorporated into prices. The model has an analytical solution to the sentiment equilibrium price. We find that sentiment trading quantity not only increases the market liquidity, but also causes the asset prices' overreaction if the intensity of sentiment demand is more than a constant value. Therefore, the continuing overreactions result in a short-term momentum and a long-term reversal. The model could offer a partial explanation to some financial anomalies such as price bubbles, high volatility, asset prices' overreaction and so on.     

The Impact of Monetary Policy and Housing-Purchase Restrictions on Housing Prices in China

This paper examines the level and volatility effect of monetary policy on housing prices in China utilizing a novel set of housing price indices constructed by (Fang, H., QuanlinGu, W. X., & Zhou, L.-A. (2015). Demystifying the Chinese housing boom. NBER Macroeconomics Annual 2015, Volume 30. University of Chicago Press.). We find that in the long-run, average housing prices react positively to inflation, money supply and bank lending growth, and negatively to the reserve requirement ratio and benchmark lending rate. Housing prices in Tier 1 cities respond more sensitively to monetary shocks relative to Tier 2 and 3 cities, possibly due to surging demand and limited supply under housing-purchase restrictions (HPR). We further study the volatility effect of monetary shocks using the GARCH model and find that the benchmark lending rate, reserve requirement ratio and money supply growth have strong negative impact on the volatility of housing price growth. Our benchmark results remain robust after incorporating the HPR policy variable in the estimation, with a significant negative effect of HPR on housing price growth in Tier 1 and Tier 2 cities. Lastly, we conclude with recommendations on future monetary policy design and implementation, with a specific focus on the heterogeneous characteristics of China’s housing market.     

Using time-varying transition probabilities in Markov switching processes to adjust US fiscal policy for asset prices

This paper tests for nonlinear effects of asset prices on the US fiscal policy. By modeling government spending and taxes as time-varying transition probability Markovian processes (TVPMS), we find that taxes significantly adjust in a nonlinear fashion to asset prices. In particular, taxes respond to housing and (to a smaller extent) to stock price changes during normal times. However, at periods characterized by high financial volatility, government taxation only counteracts stock market developments (and not the dynamics of the housing sector). As for government spending, it is neutral vis-a-vis the asset market cycles. We conclude that, correcting the fiscal balance and, notably, the revenue side for time-varying effects of asset prices provides a more accurate assessment of the fiscal stance and its sustainability.     

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.