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.     

Empirical of the Taiwan stock index option price forecasting model – applied artificial neural network

This work presents a novel neural network model for forecasting option prices using past volatilities and other options market factors. Out of different approaches to estimating volatility in the option pricing model, this study uses backpropagation neural network to forecast prices for Taiwanese stock index options. The ability to develop accurate forecasts of grey prediction volatility enables practitioners to establish an appropriate hedging strategy at in-the-money option.     

A comparison of pricing and hedging performances of equity derivatives models

This article investigates the pricing/hedging conundrum, i.e. the observation of a mismatch between derivatives models’ pricing and hedging performances, that has so far been under-emphasized as the literature tends to focus on increasingly complicated option pricing models, without adequately addressing hedging performance. Hence, we analyse the ability of the Black–Scholes, Practitioner Black–Scholes, Heston–Nandi and Heston models to Delta-hedge a set of call options on the S&P500 index and Apple stock. We extend earlier studies in that we consider the impact of asset dynamics, apply a stringent payoff replication strategy, look at the impact of moneyness at maturity and test for the robustness to the parameters’ calibration frequency and Delta-Vega hedging. The study shows that adding risk factors to a model, as stochastic volatility, should only be considered in light of the data dynamics. Even then, however, more complicated models generally fare poorly for hedging purposes. Hence, a better fit of a model to option prices is not a good indicator of its hedging performance, and so of its ability to describe the underlying dynamics. This can be understood for reasons of over-fitting. Those findings hint to a potentially appealing hedging-based calibration of models’ parameters, rather than the standard pricing-based one.     

Pricing bond options under a Markovian regime-switching Hull–White model

In this paper, we investigate the valuation of bond options under a Markovian regime-switching Hull–White model, where both the mean-reverting level and the volatility of the interest rate are modulated by a continuous-time, finite-state Markov chain. Using techniques of measure changes and the inverse Fourier transform, we obtain an integral representation for the pricing formula of a standard European option on a zero-coupon bond. Numerical results for the prices and implied volatilities of bond options arising in our model are given in a two-regime case.     

An improved framework for approximating option prices with application to option portfolio hedging

As the price of the underlying asset changes over time, delta of the option changes and a gamma hedge is required along with delta hedge to reduce risk. This paper develops an improved framework to compute delta and gamma values with the average of a range of underlying prices rather than at the conventional fixed ‘one point’. We find that models with time-varying volatility price options satisfactorily, and perform remarkably well in combination with the delta and delta-gamma approximations. Significant improvements are achieved for the GARCH model followed by stochastic volatility models. The new approach can ensure significant improvement in modelling option prices leading to better risk-management decision-making.     

The adequacy of volatility for the elaboration of technology valuation based on real options

When evaluating the economic value of a technology or business project, we need to consider the period and cost for commercialisation. Since the discounted cash flow (DCF) method has limitations in that it can not consider consecutive investments or does not reflect the probabilistic property of commercialisation cost, we often take it desirable to apply the concept of real options with key metrics of underlying asset value, commercialisation cost, and volatility, while regarding the value of technology and investment as the opportunity value. We provide more elaborated real options model, which reflects the uncertainty in the option pricing model (OPM).     

Equilibrium asset pricing under the Lévy process with stochastic volatility and moment risk premiums

In this paper, we extend Zhang, Zhao and Chang's (2012) production-based equilibrium asset pricing model from a jump diffusion setting to a Lévy process with stochastic volatility. This paper is a further extension of Fu and Yang (2012), which is under a Lévy process with a constant volatility. Using newly developed closed-form formulas of equity premium and pricing kernel, we are able to price Schouten's (2005) moment swaps analytically. Numerical results show that our pricing formula performs very well. Our model explains Zhao, Zhang and Chang's (2013) empirical observations on moment risk premiums.     

基于Poisson跳跃的信用价差期权定价

信用价差是用以向投资者补偿参照资产违约风险的、高于无风险利率的利差。信用价差期权作为风险控制的重要手段之一,其定价也日益得到人们的关注。现有文献几乎是单纯地利用几何布朗运动来刻画资产的价格变化过程从而对信用价差期权进行定价。而在实际中会出现某些不寻常的事件导致资产价格出现不间断的跳跃现象,普通的定价方法对这种现象的解释力度不够。因此本文引入Poisson跳跃来描述信用价差变化过程中的异常情况,更好地解释当遇到金融危机等情况时资产价值的跳跃现象。由于Longstaff和Schwartz的模型引入了随机利率,可以给出定价公式的封闭解析解的优点,本文在此模型上进行进行研究,将刻画信用价差动态过程的O-U过程与Poisson跳跃结合,利用伊藤公式进行推导并引入了利率的平方根过程,得到了欧式信用价差期权的定价公式,更好地考虑了资产价格的跳跃情况。     

Dynamic asset pricing model with heterogeneous sentiments

The systematic and important role of investor sentiment has been supported by some recent empirical and theoretical literatures. In this paper, we present a dynamic asset pricing model with heterogeneous sentiments and we find that the equilibrium stock price is the wealth-share-weighted average of the stock prices that would prevail in an economy with one sentiment investor only. Moreover, heterogeneous sentiments induce fluctuations in the wealth distribution, which increases stock return volatility and induces mean reversion in stock returns. The model offers a partial explanation for the financial anomaly of mean reversion.     

A risk index to model uncertain portfolio investment with options

This paper models the portfolio investment performance with options by using a risk index, which is defined as the average loss below the risk-free interest rate. Using a risk-free interest rate as the uniform reference rate for all portfolios, the risk index offers an easier-to-compare loss value than the value-at-risk return, where portfolio specific references are used to calculate the average losses. Besides, uncertainty theory is used in the paper to derive the portfolio decision when stock prices are subject to experts' estimations. By analytical computation and empirical analysis, we find that portfolios considering options generate better return than the ones without options. The empirical analysis reveals that the options can effectively hedge the risk, and the call option with a higher exercise price offers higher return per unit of option premium. Furthermore, our proposed model produces higher expected return in most cases than the model where the risk is measured by the chance of the total return failing to reach the threshold level of return.     

Investor sentiment,information and asset pricing model

We present an asset pricing model with investor sentiment and information, which shows that the investor sentiment has a systematic and significant impact on the asset price. The equilibrium price's rational term drives the asset price to the rational, and the sentiment term leads to the asset price deviating from it. In our model, the proportion of sentiment investors and the information quality could amplify the sentiment shock on the asset price. Finally, the information is fully incorporated into prices when sentiment investors learn from prices. The model could offer a partial explanation of some financial anomalies: price bubbles, high volatility, asset prices' momentum effect and reversal effect.     

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.     

Ad-Hoc Black–Scholes vis-à-vis TSRV-based Black–Scholes: Evidence from Indian Options Market

This research paper examines one-day-ahead out-of-sample performance of the volatility smirk-based options pricing models, namely, Ad-Hoc-Black–Scholes (AHBS) models on the CNX Nifty index options of India. Further, we compare the performance of these models with that of a TSRV-based Black–Scholes (BS) model. For the purpose, the study uses tick-by-tick data. The results on the AHBS models are highly satisfactory and robust across all the subgroups considered in the study. Notably, a daily constant implied volatility based ad-hoc approach outperforms the TSRV-based BS model substantially. The performance of the ad-hoc approaches improves further when the smile/smirk effect is considered. For the estimation of the implied volatility smile, we apply three weighting schemes based on the Vega and liquidity of the options. All the schemes offer equally competing results. The major contribution of the study to the existing literature on options pricing is in terms of the ex-ante examination of the ad-hoc approaches to price the options by calibrating volatility smile/smirk on a daily basis.

     

Asset pricing theory and the valuation of Canadian paintings

Abstract.  The valuation of Canadian paintings is analysed empirically. Using a sample of auction prices for major Canadian painters for the period 1968–2001, we run hedonic regressions to analyse the influence of various factors, including painter identity, on auction prices, as well as to construct a market price index. This index is used in a second‐stage analysis in which we analyse the properties of Canadian art viewed as an investment asset. We apply standard asset pricing theory, as incorporated in the capital asset pricing model (CAPM), to the analysis of price movements in the market for Canadian paintings.     

Prediction of volatility based on realized-GARCH-kernel-type models: Evidence from China and the U.S.

We propose three Realized-GARCH-Kernel-type models which do not make the distribution assumptions on the return disturbance terms. We use this type of model to predict the return volatilities of the 50ETF in China and the S&P500 index in the U.S. The semiparametric kernel density estimator of our models, which captures the skewness, asymmetry and fat-tail of financial assets, performs well both statistically and economically. Our models have more predictive power than other eight comparable volatility models that need to pre-specify the distribution of the disturbance terms. Our results are robust to eight measures of realized volatility. Using option straddle strategies, we show that our models generate larger trading profits and greater Sharpe ratios than the other competing models.     

异质信念资产定价研究

从随机游走、行为金融到混沌，从现代资产定价理论、行为资产定价理论到异质信念资产定价理论，3种学说和3种定价理论同时存在干当今资本市场的研究中，它们分别从不同方面、不同视角解释了资产价格的波动。本文的研究理清了3种重要定价理论之间的关系：理性与有限理性，线性与非线性，价格波动的外在机制与内在机制，为人们进一步研究资产定价理论提供了清晰的脉络。     

Pricing foreign equity options with regime-switching

In this paper, we investigate the valuation of two types of foreign equity options under a Markovian regime-switching mean-reversion lognormal model, where some key model parameters in the dynamics of the foreign equity price and the foreign exchange rate are modulated by a continuous-time, finite-state Markov chain. A fast Fourier transform (FFT) approach is applied to provide an efficient way to evaluate the option prices. Numerical analysis and empirical studies are provided to illustrate the practical implementation of the proposed pricing model.     

STOCK PRICE VOLATILITY,NEGATIVE AUTOCORRELATION AND THE CONSUMPTION–WEALTH RATIO: THE CASE OF CONSTANT FUNDAMENTALS

Based on infinite horizon models, previous theoretical works show that the empirical stock price movement is not justified by the changes in dividends. The present paper provides a simple overlapping generations model with constant fundamentals in which the stock price displays volatility and negative autocorrelation even without changes in dividend. The horizon of the agents matters. In addition, as in recent empirical works, the aggregate consumption–wealth ratio ‘predicts’ the asset return. Thus, this framework may be useful in understanding different stylized facts in asset pricing. Directions for future research are also discussed.     

A semiparametric estimation of liquidity effects on option pricing

Abstract. This paper proposes a semiparametric option pricing model with liquidity, as proxied by the relative bid-ask spread. A nonparametric volatility function with liquidity costs as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. The SNN estimator is particularly suitable for the characteristics of option data in financial markets. Moreover, we propose a natural extension of the univariate bandwidth parameter optimal estimation to the multivariate case. A statistical design to test competing option pricing models which takes into account the lack of independence between them is also presented. The in-sample performance of the model turns out to be statistically favorable relative to the competing model without liquidity. Also, an additional experiment is performed within sample, but with just a subsample of options not employed in the nonparametric estimation of the implied volatility function being priced. The results are also favorable to our semiparametic theoretical option pricing model with liquidity. However, the out-of-sample performance is quite disappointing regardless of what option pricing model is employed in the estimation. Eva Ferreira and Gonzalo Rubio acknowledge the financial support provided by Dirección Interministerial Científica y Técnica (DGICYT) grants PB98-0149 and PB97-0621 respectively. All three authors aknowledge the financial support provided by Universidad del País Vasco (UPV/EHU) grant UPV 038.321-HA129/99, and the BSI Gamma Foundation. We appreciate the helpful comments of two anonymous referees, ángel León, José M. Campa, Fernando Tusell and Javier Fernández Navas, seminar participants at the Bank of Spain and the European Financial Management Association (Athens), and the computational assistance of Gregorio Serna. We thank Juan Ayuso and MEFF for providing the data used in this article. The contents of this paper are the sole responsability of the authors.     

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.