The Difference Between Foreign Deflators and the Foreign Cash Roll Up: Implications for Risk-Neutral
Document ID: 2008-95 (previously 2008/03)
Published on: 1st April 2008
When running a multi-currency risk-neutral valuation, care must be taken to ensure that cash flows in different currencies are discounted correctly. As explained in Technical Note 2004/04, Currency Model Specification, “foreign” cash flows, i.e. those expressed in a currency other than the “base currency”, should be discounted by their local “foreign deflator”. This is defined as the base-currency cash rollup, modified by some currency translation. However, in certain circumstances it can be shown that this is equivalent to simply discounting at the foreign currency cash rollup. In summary, provided the exchange rate is independent of the foreign cash flow, it is valid to use the foreign cash rollup rather than the foreign deflator. Indeed using the foreign deflator simply introduces additional noise, i.e. sampling error, into the valuation.
