Description

This research has two major contributions. First, our study expands existing FRM papers in the economic interpretation of the risk index. Supported by simulation based empirical tests, Zbonakova, Härdle, and Wang (2017) show that index depends on three major factors: the variance of the error term, the correlation structure of the covariates and the number of non-zero coefficients of the model. Ren, Lu, Li, and Härdle (2022) and Wang, Althof, and Härdle (2023) further extend it by adding Lagrange interpretation. Based on their analysis, this work offering both empirical and analytical evidence of the correlation between FRM index and the pricing kernel’s volatility.

Second, our study proves that FRM reflects forward-looking risk information in cryptocurrencies. The option markets for cryptocurrencies are less mature in comparison to more established assets such as equities. Therefore, calculating the risk-neutral distribution used to price these assets presents greater complexity, and even when a reliable risk neutral distribution is available, it is still difficult to estimate the physical distribution due to the lack of the characteristic information of the marginal investors. As a result, obtaining forward-looking risk estimates from the option market is challenging. In this particular context, we employ FRM to compute the spread between in-sample and out-of-sample predictability to derive forward-looking insights within the realm of cryptocurrencies.