# Tag Info

The state price vector are the prices of securities which pay \$1 if and only if that state of the world occurs. This is just a question of being able to replicate the payoffs $$\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$$ with payoff vectors$\vec{b} = [1,1,1]^T$and ... 1 these kinds of questions usually require careful attention to details: if it's a hw question of some kind, consult shreve's lecture notes, he has a whole section on this precise topic in all its glory. as for intuition, since holding$\frac{\partial \xi}{\partial S}$at any point in time eliminates the dW term, in the context of a discrete time period model ... 1 definition of a variance swap is$ \int^{T+\Delta}_T \mathbb{E}_t[v_s] ds $where$v_s$is the variance and$\mathbb{E}_t[v_s]$is the expectation of the variance of time s at time t. therefore, pnl is:$ (\int^{T+\Delta}_T \mathbb{E}_t[v_s] ds - \int^{T+\Delta}_{T} \mathbb{E}_{t-\delta}[v_s] ds)*d\delta \$