Young Economics

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Economics
overview:notation

Greek Letters

A A $\alpha$ 1 alpha
B B $\gamma$ 2 beta
C X $\chi$ 22 chi
D $\Delta$ $\delta$ 4 delta
E E $\epsilon$ 5 epsilon
F $\Phi$ $\phi$ 21 phi
G $\Gamma$ $\gamma$ 3 gamma
H H $\eta$ 7 eta
I I $\iota$ 9 iota
J
K K $\kappa$ 10 kappa
L $\Lambda$ $\lambda$ 11 lambda
M M $\mu$ 12 mu
N N $\nu$ 13 nu
O O o 15 omicron
P $\Pi$ $\pi$ 16 pi
Q $\Theta$ $\theta$ 8 theta
R P $\rho$ 17 rho
S $\Sigma$ $\sigma$ 18 sigma
T T $\tau$ 19 tau
U $\Upsilon$ $\upsilon$ 20 upsilon
V
W $\Omega$ $\omega$ 24 omega
X $\Xi$ $\xi$ 14 xi
Y $\Psi$ $\psi$ 23 psi
Z Z $\zeta$ 6 zeta

Pricing Equation with Discount Factor

I follow a discount factor/GMM view of asset pricing theory (Cochran [2012]), which can be summarized by two equations: \begin{eqnarray*} p_t & = &E(m_{t+1} x_{t+1}) \\ m_{t+1} &=& f(data,parameters) \end{eqnarray*}

where $p_t$ = asset price, $x_{t+1}$ = asset payoff, $m_{t+1}$ = stochastic discount factor.

Price, Payoffs, and Notation

The price $p_t$ gives rights to a payoff $x_{t+1}$.

 price $p_t$ payoff $x_{t+1}$ $p_t$ $p_t+d_{t+1}$ 1 $R_{t+1}$ 1 $R^f$ $\frac{p_t}{d_t}$ $\frac{p_{t+1}+d_{t+1}}{d_t}$ C $max(S_T - K, 0)$

Notation

• Vectors or matrices are written in Capital letters (e.g. $X_t$), whereas scalars are written in lower letters (e.g. $r_t$)
• $P_t$ = Price of asset at t
• $c_t$ = Consumption. but sometimes may indicate Price of Contingent Claims, such as call option.
• $x_{t+1}$ = Payoff at $t+1$
• $m_{t+1}$ = stochastic discounting factor