We propose a new uncertainty index based on the discrepancy of the smile of FX options. We show that our index spikes near turbulent periods, forecasts economic activity and its innovations hold a significant and negative equity premium. Unlike other uncertainty indexes, our index is supported by equilibrium models, which relate the difference of options prices across moneyness to uncertainty. Moreover, our index is based on investment decisions, can be easily and continuously updated and is comparable across countries.
ResumoO objetivo deste trabalho é o de avaliar o efeito da dimensionalidade e da probabilidade de exercício de uma opção de compra européia, no ganho de precisão obtido com o uso da Amostragem Descritiva no apreçamento destas opções através de Simulação Monte Carlo, em lugar da abordagem tradicional da Amostragem Aleatória Simples. Após confirmar a ausência de viés nas estimativas, sua precisão foi avaliada pelo erro padrão destas estimativas. Os resultados obtidos mostram que a eficiência estatística das duas técnicas não é afetada pelo aumento da dimensionalidade do problema, não sofrendo perda de precisão com esta variação. No entanto, em relação ao preço de exercício, embora a Amostragem Descritiva tenha se mostrado mais eficiente do que a Amostragem Aleatória Simples, observou-se uma redução do ganho de precisão à medida que a probabilidade de exercício diminui. Embora os resultados aqui apresentados se atenham ao caso particular de uma opção européia, há evidências de que o mesmo tipo de comportamento em relação à dimensionalidade do problema e à probabilidade de exercício também se manifeste nos demais tipos de opção.Palavras-chave: simulação de Monte Carlo; amostragem descritiva; opção.
AbstractThe purpose of this paper is to evaluate the effect of dimensionality and probability of exercise of a European call option on the precision improvements obtained by the usage of Descriptive Sampling on a Monte Carlo Simulation to price such derivative as opposed to the use of traditional Simple Random Sampling. After verifying the absence of bias, the precision of the estimates was assessed by their standard error. The results show that the statistical efficiency of both techniques is unaffected by an increase of dimensionality and maintain their level of precision. However, as to the exercise price, although Descriptive Sampling proved to be more efficient than Simple Random Sampling, the improvement weakens as the option's exercise probability declines. Although this work relates to European options, other options should behave similarly in regard to dimensionality and exercise price.
The purpose of this paper is to measure the impact of interest rate decisions of the Monetary Policy Committee (MPC) on foreign exchange (FX) rate in Brazil. Two new daily measures of interest rate surprises are proposed using market and survey data. The results indicate a significant effect of MPC's decisions on FX returns. In particular, the surprise variable based on market data is statistically significant to explain FX returns and has a negative sign, as expected (a positive surprise implies an appreciation of the domestic currency). Moreover, this effect is symmetric, in terms of positive or negative surprises, and does not depend on the level of Selic interest rate. Nonetheless, the surprise variable is not significant to explain FX returns in recent years, under a single-digit interest rate regime. Robustness exercises—using GARCH models or including FX market official intervention series as additional controls—corroborate the previous findings.
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