2016 Summer.Includes bibliographical references.Most of the attacks on computer systems and networks are enabled by vulnerabilities in a software. Assessing the security risk associated with those vulnerabilities is important. Risk mod- els such as the Common Vulnerability Scoring System (CVSS), Open Web Application Security Project (OWASP) and Common Weakness Scoring System (CWSS) have been used to qualitatively assess the security risk presented by a vulnerability. CVSS metrics are the de facto standard and its metrics need to be independently evaluated. In this dissertation, we propose using a quantitative approach that uses an actual data, mathematical and statistical modeling, data analysis, and measurement. We have introduced a novel vulnerability discovery model, Folded model, that estimates the risk of vulnerability discovery based on the number of residual vulnerabilities in a given software. In addition to estimating the risk of vulnerabilities discovery of a whole system, this dissertation has furthermore introduced a novel metrics termed time to vulnerability discovery to assess the risk of an individual vulnerability discovery. We also have proposed a novel vulnerability exploitability risk measure termed Structural Severity. It is based on software properties, namely attack entry points, vulnerability location, the presence of the dangerous system calls, and reachability analysis. In addition to measurement, this dissertation has also proposed predicting vulnerability exploitability risk using internal software metrics. We have also proposed two approaches for evaluating CVSS Base metrics. Using the availability of exploits, we first have evaluated the performance of the CVSS Exploitability factor and have compared its performance to Microsoft (MS) rating system. The results showed that exploitability metrics of CVSS and MS have a high false positive rate. This finding has motivated us to conduct further investigation. To that end, we have introduced vulnerability reward programs (VRPs) as a novel ground truth to evaluate the CVSS Base scores. The results show that the notable lack of exploits for high severity vulnerabilities may be the result of prioritized fixing of vulnerabilities
