Counterparty Credit Risk, Collateral and Funding: With Pricing Cases For All Asset Classes (The Wiley Finance Series) by Damiano Brigo & Massimo Morini & Andrea Pallavicini

Author:Damiano Brigo & Massimo Morini & Andrea Pallavicini [Brigo, Damiano]
Language: eng
Format: mobi
ISBN: 9780470661673
Publisher: Wiley
Published: 2013-02-27T18:30:00+00:00

with and adapted processes and W a Brownian motion under the domestic risk-neutral measure with numeraire Bd, then (9.6) considered over all possible T and T implies

saying that the drift of the rate to exchange the foreign currency with the domestic one under the risk-neutral measure of the domestic currency is the difference between the risk-free rate of the domestic currency and that of the foreign one, a well-known result, for example, see [48]. An immediate informal proof may be obtained by taking T = t+dt for vanishingly small dt. This no-arbitrage relation, that applies to a world of risk-free discount rates, will be useful later when it comes to understanding the presence of the basis in collateralized CCS.

The second point to make on (9.3) and (9.4) is that these relations look like a change of numeraire, and they are telling us which numeraires we have to consider if we want to treat this change of measure exactly as a change of numeraire. As shown in [48], we are moving between numeraire Bft, the foreign bank account, and numeraire , the domestic bank account expressed in foreign currency, or equivalently between numeraire , the foreign bank account expressed in domestic currency, and numeraire Bt, the domestic bank account. The latter expression has the advantage of not altering our definition of the domestic risk-neutral measure, and we will follow this. Obviously, we need to express quantities in the same currency asymmetry in the valuation. heterministicdiscreted for finding no-arbitrage relationships.

The above relationships can be summarized saying that Xftis a foreign tradable asset IFF is a domestic tradable asset.

For forward measures, a chain of measure changes leads to

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