Introduction

In the aftermath of the global financial crisis of 2008, massive regulations were imposed on investment banks, forcing them to conduct frequent, heavy regulatory calculations. While these regulations made it harder for banks to conduct derivatives businesses, they also contributed to a new golden age of computational finance.

A typical example of regulatory calculation is the CVA (Counterparty Value Adjustment),1 an estimation of the loss subsequent to a future default of a counterparty when the value of the sum of all transactions against that counterparty (called netting set) is positive, and, therefore, lost. The CVA is actually the value of a real option a bank gives away whenever it trades with a defaultable counterparty. This option is a put on the netting set, contingent on default. It is an exotic option, and a particularly complex one, since the underlying asset is the netting set, consisting itself in thousands of transactions, some of which may be themselves optional or exotic. In addition, the netting set typically includes derivatives transactions in different currencies on various underlying assets belonging to different asset classes. Options on a set of heterogeneous underlying assets are known to the derivatives industry and called hybrid options. Investment banks' quantitative research departments actively developed hybrid models and related numerical implementations in the decade 1998–2008 for the risk management of very profitable transactions ...

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