Option Pricing

Symbol Definition
\(S(t)\) Stock Price at time \(t\)
\(C(t)\) Call Option Price at time \(t\)
\(P(t)\) Put Option Price at time \(t\)
\(E\) Strike Price
\(T\) Expiry time

At expiry

\[\begin{align} C(T) = max(S(T) - E, 0) \\ P(T) = max(E - S(T), 0) \end{align}\]

Put-call parity

\[ C(t) - P(t) = S(t) - Ee^{-r(T-t)} \]