On a symmetrization of diffusion processes

The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion processes. The present paper aims to give a basis to the use of the numerical scheme for Heston and SABR-type stochastic volatility models. This will be done by showing a fairly general result on the symmetrization (in multi-dimension/multi-reflections). Further applications (to time-inhomogeneous diffusions/ to time-dependent boundaries/to curved boundaries) are also discussed.     

Implied integrated variance and hedging

If the volatility is stochastic, stock price returns and European option prices depend on the time average of the variance, i.e. the integrated variance, not on the path of the volatility. Applying a Bayesian statistical approach, we compute a forward-looking estimate of this variance, an option-implied integrated variance. Simultaneously, we obtain estimates of the correlation coefficient between stock price and volatility shocks, and of the parameters of the volatility process. Due to the convexity of the Black–Scholes formula with respect to the volatility, pricing and hedging with Black–Scholes-type formulas and the implied volatility often lead to inaccuracies if the volatility is stochastic. Theoretically, this problem can be avoided by using Hull–White-type option pricing and hedging formulas and the integrated variance. We use the implied integrated variance and Hull–White-type formulas to hedge European options and certain volatility derivatives.     

Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

This paper develops two novel methodologies for pricing and hedging European-style barrier option contracts under the jump to default extended constant elasticity of variance (JDCEV) model, namely: a stopping time approach based on the first passage time densities of the underlying asset price process through the barrier levels; and a static hedging portfolio approach in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. In doing so, both valuation methodologies are extended to a more general set-up accommodating endogenous bankruptcy, time-dependent barriers and the commonly observed stylized facts of a positive link between default and equity volatility and of a negative link between volatility and stock price. The two proposed numerical methods are shown to be accurate, easy to implement and efficient under both the JDCEV model and the nested constant elasticity of variance model.     

Valuación de opciones de tipo de cambio asumiendo distribuciones α-estables

This paper aims to present the valuation of options using the Black-Scholes method assuming α-stable distributions as an alternative option valuation in the Mexican market. The use of α-stable distributions for modelling financial series allows to overcome the classical valuation main weakness which assumes normality, by capturing the presence of heavy tails and asymmetry in financial time series. One of the main results is the price differential between the two models and the effect of alpha and beta parameters on prices; to show the difference valuation is made of a call option and a put option for the peso-dollar exchange rate. Likewise, basic sensitivity measurements of options (delta, gamma, and rho) were made and the effect of the stability parameter (α) was made on the implied volatility of options assuming the α-stable price as the market price.     

Optimal dividend policies for piecewise-deterministic compound Poisson risk models

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.     

Valuing executive stock options: performance hurdles, early exercise and stochastic volatility

Accounting standards require companies to assess the fair value of any stock options granted to executives and employees. We develop a model for accurately valuing executive and employee stock options, focusing on performance hurdles, early exercise and uncertain volatility. We apply the model in two case studies and show that properly computed fair values can be significantly lower than traditional Black–Scholes values. We then explore the implications for pay-for-performance sensitivity and the design of effective share-based incentive schemes. We find that performance hurdles can require a much greater fraction of total compensation to be a fixed salary, if pre-existing incentive levels are to be maintained.     

Are executive stock option exercises driven by private information?

In this study, we investigate the extent to which exercise of executive stock options is based upon private information. Contrary to popular belief, we find that shares are held more than 30 days following over a quarter of options exercised. Partitioning the data, we find weak evidence that decisions to exercise and sell immediately are prompted by bad news and stronger evidence that decisions to exercise and hold for at least 30 days are prompted by good news. Enhancing the power of our tests by considering several factors important to exercise decisions, we find that the higher the opportunity costs of early exercise as measured by the time-value of options, the greater the trading profits to executives. We also find that the greater the disguise provided by incentives to diversify and consume as measured by the depth of options in the money, the greater the trading profits to executives who exercise and sell. Turning to non-exercise decisions, we find that a strategy of holding options rather than shares to exploit good news yields positive abnormal returns consistent with theoretical predictions in the absence of dividends.

VIX期权定价与校正

VIX期权作为波动率衍生品能为金融机构提供有效的市场风险对冲工具。文献中对VIX期权定价的实证分析误差都很大,原因在于模型的选取误差以及校正方法和样本选取不妥。通过在VIX模型中加入均值回复因素和跳因素,可以使VIX过程更加合理,也可以使VIX期权定价精度更高。通过对VIX期权市场中间报价进行校正,得到了4个文献模型的参数估计,并比较4个模型的定价精度和正向隐含波动率偏斜拟合效果。     

Growth to value: Option exercise and the cross section of equity returns

We propose a general equilibrium model to study the link between the cross section of expected returns and book-to-market characteristics. We model two primitive assets: value assets and growth assets that are options on assets in place. The cost of option exercise, which is endogenously determined in equilibrium, is highly procyclical and acts as a hedge against risks in assets in place. Consequently, growth options are less risky than value assets, and the model features a value premium. Our model incorporates long-run risks in aggregate consumption and replicates the empirical failure of the conditional capital asset pricing model (CAPM) prediction. The model also quantitatively accounts for the pattern in mean returns on book-to-market sorted portfolios, the magnitude of the CAPM-alphas, and other stylized features of the cross-sectional data.     

Is the relationship between investment and conditional cash flow volatility ambiguous,asymmetric or both?

We investigate the effect of cash flow volatility on investment. Our evidence suggests that financially constrained firms decrease investment (i) when experiencing persistently high volatility; (ii) when experiencing both high volatility and negative cash flow growth realisations; and (iii) when holding low cash levels and experiencing both high volatility and a negative cash flow growth realisations. In financially unconstrained firms, the above effects are either not found or are of relatively low economic importance. Overall, our findings lend support to the financial flexibility literature and tend to contradict predictions of the real options literature.