Multi-curve bootstrapping and implied discounting curves in illiquid markets

• Main Author: Sender, Nina Alexandra
• Other Authors: Taylor, David
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2017
• Subjects: Mathematical Finance
• Online Access: http://hdl.handle.net/11427/25447

The credit and liquidity crisis of 2007 has triggered a number of inconsistencies in the interest rate market, questioning some of the standard methods and assumptions used to price and hedge interest rate derivatives. It has been shown that using a single risk-free curve (constructed from market instruments referencing underlying rates of varying tenors) to forecast and discount cash flows is not theoretically correct. Standard market practice has evolved to a multi-curve approach, using different curves to forecast and discount cash flows. The risk-free discount curve is proxied by the Overnight-Indexed Swap (OIS) curve. In South Africa there is no liquid market for OIS. In this dissertation a method is developed to estimate the ZAR OIS curve. A cointegration relationship between the SAFEX Overnight Rate, and the 3-month JIBAR rate is shown to exist. This relationship is used in a dual bootstrap algorithm, to simultaneously estimate the ZAR OIS curve and 3-month JIBAR tenor curve, while maintaining arbitrage relationships. The tractability of this method is shown, by pricing options written on ZAR OIS.