Asset-or-nothing Option Valuation in the Black and Scholes model

Question

In standard Black-Scholes Model, compute the price of an asset-or-nothing put and asset-or-nothing call options. Write down the put-call parity relation between the asset-or-nothing call and put option prices.

Answer 1

the answer for calculating the prices can be found here - see chapter: Black–Scholes valuation ;)

The put-call parity in that case is pretty straight forward: $P=Se^{-qT}-C$. Using the results presented on the Wikipedia page in the aforementioned section this can be proved as follows

$P=Se^{-qT}-C$

$=Se^{-qT}-Se^{-qT}\Phi(d_1)$

$=Se^{-qT}(1-\Phi(d_1))=Se^{-qT}\Phi(-d_1)$