Which implied volatility provides the best measure of future volatility?

The volatility smile/skew phenomenon makes it unclear which implied volatility provides the best measure of the market volatility expectation over the remaining life of the option. Due to the high liquidity of at-the-money option and the low sensitivity of its implied volatility to the price error, the at-the-money implied volatility is often considered a good measure of future volatility. In this paper, we raise the question: is at-the-money implied volatility the best we can do? We provide in this paper an analytical rationale that the implied volatility from option with highest vega outperforms the at-the-money implied volatility in terms of forecasting ability, especially for long forecasting horizons. Our empirical findings are consistent with our theoretical argument.     

Options and earnings announcements: an empirical study for the European Options Exchange

In this paper we give an introduction in option pricing theory and explicitly specify the Black-Scholes model. Although market participants use this and similar models to price options, they violate one of the fundamental assumptions of the model. They do not set a constant value for the volatility of the underlying asset over time, but change the volatility even during a day. By means of event study methodology we investigate the volatility of the underlying asset and the volatility implicit in option prices around earnings announcements by firms. We find that the volatility in option prices increases before the announcement date and drops sharply afterwards. The volatility of the underlying stocks is higher only at the announcement dates and we do not observe a higher volatility around these dates. Hence, the constant volatility of the underlying asset, which is one of the assumptions in the Black-Scholes model, does not hold. However, the market seems to correctly anticipate the change in volatility, by correcting option prices.     

基于实物期权法的风险投资项目估价方法——一个文献综述

本文理清了实物期权及其在风险投资项目估价中应用的发展脉络,并提出了实物期权在风险投资项目估价应用中需要发展的地方。     

Joint dynamic modeling and option pricing in incomplete derivative-security market

In this study, we evaluate the option prices on two assets under stochastic interest rates when the stochastic process that underlying asset prices follow is depending on a correlated bivariate Markov-modulated geometric Brownian motion model with jump risks. More specifically, we conduct the joint dynamic modeling by identifying two independent compound Poisson processes with the log-normal jump sizes to describe both individual jumps and systematic cojumps. Facilitating the cojumping behavior this way with the time-inhomogeneity of the volatility, option pricing expressions are readily obtainable since the Gerber–Siu’s approach is employed to determine a pricing kernel. The empirical results and numerical illustrations are provided to show the impact of cojumps and stochastic volatilities on option prices.     

A real options approach to valuing and negotiating licensing agreements

We apply real options modeling to a common pharmaceutical industry licensing arrangement to take into account various uncertainties and the flexibility value. The managerial flexibility is limited to the project abandonment option. We extend previous work by incorporating the phases required to bring the project from patent approval to market. We also incorporate a deterministic variable into the cash flow process that provides a realistic product lifecycle. We focus on the allocation of project value between licensor and licensee, i.e., the so-called “profit split” ratio (PSR) because it is commonly used in practice to negotiate terms. We find: (1) Ignoring the managerial flexibility in valuation may cause the licensee to either forego an acceptable deal or enter into an inferior deal. (2) The magnitude of project profitability as well as cost and sales uncertainty affects the licensor's bargaining power over compensation for granting abandonment flexibility to the licensee. (3) Managers must exercise care when estimating sales volatility because the flexibility value is more sensitive to sales volatility than it is to cost volatility. (4) Failure to incorporate the product lifecycle will produce suboptimal capital investment decisions.     

Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options

In this paper, we evaluate the performance of the ability of Markov-switching multifractal (MSM), implied, GARCH, and historical volatilities to predict realized volatility for both the S&P 100 index and equity options. Some important findings are as follows. First, we find that the ability of MSM and GARCH volatilities to predict realized volatility is better than that of implied and historical volatilities for both the index and equity options. Second, equity option volatility is more difficult to be forecast than index option volatility. Third, both index and equity option volatilities can be better forecast during non-global financial crisis periods than during global financial crisis periods. Fourth, equity option volatility exhibits distinct patterns conditional on various equity and option characteristics and its predictability by MSM and implied volatilities depends on these characteristics. And finally, we find that MSM volatility outperforms implied volatility in predicting equity option volatility conditional on various equity and option characteristics.     

Shadow costs of incomplete information and short sales in the valuation of the firm and its assets

This paper presents a simple framework for the valuation of compound options within shadow costs of incomplete information and short sales. The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge and heterogeneous expectations. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton's (1987. Journal of Finance 42, 510) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu et al. (1996. Review of Quantitative Finance and Accounting, 7, 136) who propose an incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales.When deriving the compound call option formula, we consider a call option on a stock, which is itself an option on the assets of the firm. Our methodology incorporates shadow costs of incomplete information and short sales on the firm's assets as well as the effects of leverage in the capital structure. The formula can be useful in the valuation of several corporate liabilities in the presence of information uncertainty and short sales constraints about the firm and its cash flows. Our analysis can be used for the valuation of several real options.     

An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching

In this paper, an analytical approximation formula for pricing European options is obtained under a newly proposed hybrid model with the volatility of volatility in the Heston model following a Markov chain, the adoption of which is motivated by the empirical evidence of the existence of regime-switching in real markets. We first derive the coupled PDE (partial differential equation) system that governs the European option price, which is solved with the perturbation method. It should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved, and numerical experiments confirm that our formula could provide quite accurate option prices, especially for relatively short-tenor ones. Finally, empirical studies are carried out to show the superiority of our model based on S&P 500 returns and options with the time to expiry less than one month.     

Evidence of irreversibility in the UK property market

The real options approach to valuation of property investment suggests that various sources of uncertainty about future returns on investment have important effects on irreversible property investment decisions. Our aim in this study has been to examine how investment decisions at three main stages of the property development/investment processes respond to different sources of uncertainty. Based on the methodology developed by Episcopos (1995), the neo-classical proposition of Hartman-Abel that predicts a positive investment-uncertainty relationship is tested against that proposed by the real option theory. It is interesting to note that our empirical findings are generally consistent with the prediction of the real option theory that uncertainty increases the option value to wait for the arrival of new information thus decreasing the current investment activities. In periods of high volatility, we would expect investors in the property market to be more prudent and scale down their investment exposure to market volatility compared with periods of a relatively stable market environment.     

Steuern und Risikobereitschaft in Modellen irreversibler Investitionen

This paper provides an overview of the literature on the influence of taxation on investment behavior under uncertainty, especially under the real options paradigm. We analyze the impact of taxation on risk-taking under irreversibility. Extending the existing literature we integrate a simple tax system into a real option model. Under irreversibility and risk neutrality, raising the tax rate can either increase or reduce risk-taking. Referring to combinations of volatility and tax rate it is possible to identify conditions for an unambiguous influence of taxes on risk-taking. Numerical simulations indicate that raising the tax rate increases risk-taking under low volatility. Implementing a final withholding tax on capital income tends to reduce risky investment. Our findings confirm the well-known results under certainty and extend them with respect to uncertainty, irreversibility, and risk-taking.     

基于股票收益的期权定价与实证分析

采用两种方法对传统的期权定价参数方法进行修正。一种是利用股票对数收益率的偏度与峰度对传统的期权定价方法计算出的期权价格进行修正,另一种是通过建立GARCH模型来预测股票收益的波动率,对传统定价方法中波动率为常数的假设进行修正。选取国电CWB1(580022)权证进行实证分析,结果表明修正得出的期权价格与实际的权证价格有很大的偏差,并对这样实证结果进行解释。     

A network of options: Evaluating complex interdependent decisions under uncertainty

The present article provides a novel framework for analyzing option network problems, which is a general class of compound real option problems with an arbitrary combination of reversible and irreversible decisions. The present framework represents the interdependent structure of decisions by using a directed graph. In this framework, the option network problem is formulated as a singular stochastic control problem, whose optimality condition is then obtained as a dynamical system of generalized linear complementarity problems (GLCPs). This enables us to develop a systematic and efficient numerical method for evaluating the option value and the optimal decision policy.     

复合期权模型在矿业工程投资决策中的应用

本文介绍了复合期权的基本概念及国内外研究情况,就复合期权理论在矿业工程投资决策中的应用进行了探讨,采用geske模型并结合实例对此进行了验证。研究表明,运用复合期权理论进行矿业工程投资决策,在某种程度上能更好地反映不确定性和管理灵活性的价值。     

Calibration of stochastic volatility models: A Tikhonov regularization approach

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach with an efficient numerical algorithm to recover the risk neutral drift term of the volatility (or variance) process. In contrast to most existing literature, we do not assume that the drift term has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach. Interestingly, our empirical study reveals that the risk neutral variance processes recovered from market prices of options on S&P 500 index and EUR/USD exchange rate are indeed linearly mean-reverting.     

基于复合实物期权的煤炭绿色开采项目风险管理

针时煤炭资源开采造成的严重环境问题提出煤炭绿色开采,在分析绿色开采所面临的技术、市场、政策等风险以及这些风险与复合实物期权种类的对应关系后,结合煤炭绿色开采项目的特点对项目所含的复合实物期权进行设计构造,选取期权价值最大者,以此规避风险,取得最佳的经济效益,环境效益和社会效益.     

Model risk and option hedging

This paper presents a theoretical approach to option hedging and valuation when traders are facing model risk. Model risk is restrictively defined as the financial risk resulting from the choice of an approximating model to proxy for the true but ex-ante unknown state space of the underlying security process. A generalized model is defined for estimating the appropriate volatility markup, which is dependent on the noisiness of the volatility estimate over time. Delta neutral hedge portfolios are created using simulated S&P 500 option prices to demonstrate that using a volatility markup in the traditional binomial model reduces model risk.     

实物期权理论在钢铁企业烧结机头脱硫项目投资决策中的应用

文章提出了在烧结机头脱硫项目投资决策中引入实物期权的基本思路和模型,并讨论了实物期权模型的应用方法。     

How should a local regime-switching model be calibrated?

Local regime-switching models are a natural consequence of combining the concept of a local volatility model with that of a regime-switching model. However, even though Elliott et al. (2015) have derived a Dupire formula for a local regime-switching model, its calibration still remains a challenge, primarily due to the fact that the derived volatility function for each state involves all the state price variables whereas only one market price is available for model calibration, and a direct implementation of Elliott et al.’s formula may not yield stable results. In this paper, a closed system for option pricing and data extraction under the classical regime-switching model is proposed with a special approach, splitting one market price into two “market-implied state prices”. The success of our approach hinges on the recovery of the two local volatility functions being transformed into an optimal control problem, which is solved through the Tikhonov regularization. In addition, an efficient algorithm is proposed to obtain the optimal solution by iteration. Our numerical experiments show that different shapes of local volatility functions can be accurately and stably recovered with the newly-proposed algorithm, and this algorithm also works quite well with real market data.     

期权定价模型的离散化矩估计

在本文中,把期权定价模型中的漂移项为一个常数,波动率假定为一个Ornstein-Uhlenbeck过程,在一定的条件下,把模型转变成唯一个双线性自回归EV模型,然后对其中的m(·)函数进行离散化后,通过矩估计的方法估计m(·)函数的系数,从而得到波动率σ的矩估计。