change of numeraire

1. Use a change of numeraire and measure to verify that the value of a claim paying K if ST -rT N (-d2). (Note that this is the first term in the Black-Scholes put price. You can mimic the derivation in the text for a cash-or-nothing call.)
2. Use a change of numeraire and measure to verify that the value of a claim paying ST if ST 1). (Note that this is the second term in the Black-Scholes put price. You can mimic the derivation in the text for an asset-or-nothing call.)