In this paper, we investigate executive stock options with endogenous departure and time-varying variances. We use a “Generalized Autoregressive Conditional Heteroskedasticity” process to capture the variance process of the log stock price. In addition, we take into consideration the departure risk of the executive and assume that the probability of remaining employed has a power form of stock price ratios. After deriving the closed-form pricing formulae of executive stock options, we illustrate the effects of the departure risk on the values of executive stock options.

In this paper, we present a new pricing model for vulnerable options, with time-varying variances for each asset described by Generalized Autoregressive Conditional Heteroscedasticity processes and correlated with the return of the asset. By connecting the underlying asset and the counterparty's assets through the market factor channel, the proposed model also captures stochastic correlation between the underlying asset return and the return of the counterparty's assets. The correlation depends on the levels of the variances of both assets and the market index as well. In the proposed framework, the closed-form solution for vulnerable options is derived and numerical results are presented to investigate the impact of counterparty default risk.

In this paper, we analyze the adequacy of using GARCH as the data-generating process to model conditional volatility of stock market index rates-of-return series. Using the Hinich portmanteau bicorrelation test, we find that a GARCH formulation or any of its variants fail to provide an adequate characterization for the underlying process of the main Latin American stock market indices. Policymakers need to be careful when using autoregressive models for policy analysis and forecast because the inadequacy of GARCH models has strong implications for the pricing of stock index options, portfolio selection, and risk management. In particular, measures of spillover effects and output volatility may not be correct when GARCH-type models are used to evaluate economic policy.