The outbreak of the novel coronavirus (COVID-19) is considered an exogenous risk, which has caused unprecedented disruptions to financial and economic markets around the globe, leading to one of the fastest U.S. stock market declines in history. However, in the pastwe have seen the market recover and we can expect the market to recover again, and on this basis we assume the Standard and Poor's 500 (S  P500) index will reach a minimum before rising again in the not-too-distant future. Here we present four forecast models of the S P500 based on COVID-19 projections of deaths released on 02/04/2020 by the University of Washington and the 2-months consideration since the first confirmed case occured in USA. The decline and recovery in the index is estimated for the following three months  . The forecast is a projection of a prediction with  fluctuations described by q-gaussian distributions . Our forecast was made on the premise that : (a ) The prediction is based on a deterministic trend that follows the data available since the initial outbreak of COVID-19, and (b) fluctuations derived from the S P500 over the last 24 years. %DIFDELCMD < \end{abstract} %DIFDELCMD < %%% \\%DIF > of accuracy.
Markets are subjected to both endogenous and exogenous risks that have caused disruptions to financial and economic markets around the globe, leading eventually to fast stock market declines . In the past, markets have recovered after any economic disruption. On this basis, we focus on the outbreak of COVID-19 as a case study of an exogenous risk and analyze its impact on the Standard and Poor's 500 (S \& P500) index . We assumed that the S\&P500 index reaches a minimum before rising again in the not-too-distant future. Here we present two cases to forecast the S\& P500 index. The first case uses an estimation of expected deaths released on 02/04/2020 by the University of Washington . For the second case, it is assumed that the peak number of deaths will occur 2-months since the first confirmed case occurred in the USA. The decline and recovery in the index were estimated for the following three months after the initial point of the predicted trend . The forecast is a projection of a prediction with stochastic fluctuations described by q-gaussian diffusion process with three spatio-temporal regimes . Our forecast was made on the premise that any market response can be decomposed into an overall deterministic trend and a stochastic term. The prediction was based on the deterministic part and for this case study is approximated by the extrapolation of the S\&P500 data trend in the initial stages of the outbreak. The stochastic fluctuations have the same structure as the one derived from the past 24 years. %DIFDELCMD < \end{abstract} %DIFDELCMD < %%% A reasonable forecast was achieved with 85\\%DIF > of accuracy.
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