= Call price in an arithmetic stock model with interest
{title2=$C=(s-Ke^{-r\tau})\Phi(d)+\nu\phi(d)$}
Let $\nu=\sigma\sqrt{(1-e^{-2r\tau})/(2r)}$ and $d=(s-Ke^{-r\tau})/\nu$, where $\tau=T-t$. The displayed discounted <Gaussian> positive-part <expectation> prices a call in the <arithmetic stock model with constant volatility>. Its delta is $\Phi(d)$. The <stock> holding $C_s$ and bank-account holding $(C-sC_s)/B$ replicate the payoff with nonnegative wealth. A nonnegative discounted-wealth <supermartingale> bound proves this is the least replication capital.
Back to article page
