Explanation of common notation

Every effort has been made throughout the text to keep notation consistent, concise and logical. However, in such a technically detailed work there are inevitably occasions when it is not possible to adhere to these principles. It is hoped that on the occasions when this happens, the deviations have been adequately explained. It is also acknowledged that the notation is at times quite dense (although nowhere near the level of concision to be found in a typical textbook on financial mathematics). In this brief appendix we will give some examples of the notation and explain the rationale for it. For the most part we are dealing with situations where there are multiple obligors. An individual obligor is typically tagged by an index i (and always represented as a subscript). Usually the total number of obligors is denoted by n . Time is represented by t . Fixed-time points such as a schedule of coupon payments are denoted by the uppercase version of this. For example, the maturity of an instrument is represented as T . A fixed coupon payment date is represented by T j where j represents the index of the coupon payment (e.g. the first coupon j = 1 occurs at time T 1 and so on and T j ≤ T for all j ). A time in-between two fixed coupon dates would be represented as t ∈ [ T j − 1 , T j ]. The time of obligor defaults is always represented by τ (so obligor i defaults at time τ i ).