Modelling of financial risk using forward-looking distributions derived from contingent claims

Abstract

In this thesis, we investigate several methods for extracting the forecast distribution from historical asset returns and market-quoted option prices. Typically, risk-neutral distributions, extracted from market quoted option prices, are considered biased estimates of the forecast distribution, and therefore need to be transformed into a real-world distribution. Transformation processes often require the use of historical data and restrictive assumptions on a representative investor. Alternatively, the recovery theorem provides a theoretically appealing method to recover the real-world distribution from the risk-neutral transition probability matrix without the use of historical returns. However, estimating the risk-neutral transition probability matrix has proven to be a challenging task, as it involves solving an ill-posed problem. Therefore, we propose a regularised multivariate Markov chain in the estimation of the risk-neutral transition probability matrix to obtain a more accurate real-world forecast distribution than obtained using the univariate model.

Comparative studies on the accuracy of real-world forecast distributions are scarce in the literature. Therefore, we further backtested and compared the accuracy of the extracted distributions on the South African Top 40 index, where we found that the forward-looking real-world distribution improved forecasting in certain situations. We also proposed a forward-looking mixture model of historical and option-implied distributions to improve forecasting. Furthermore, we implemented the extracted forecast distributions in determining safe retirement withdrawal rates. In our empirical study, we showed that the use of forward-looking distributions drastically improved the success in retirement withdrawal rates.