| gemAssetPricingExample {GE} | R Documentation |
Some Examples of Asset Pricing
Description
These examples illustrate how to find the equilibrium of an asset market by the function sdm2 and by computing marginal utility of assets (see Sharpe, 2008).
Usage
gemAssetPricingExample(...)
Arguments
... |
arguments to be passed to the function sdm2. |
Value
A general equilibrium.
References
Danthine, J. P., Donaldson, J. (2005, ISBN: 9780123693808) Intermediate Financial Theory. Elsevier Academic Press.
Sharpe, William F. (2008, ISBN: 9780691138503) Investors and Markets: Portfolio Choices, Asset Prices, and Investment Advice. Princeton University Press.
Xu Gao (2018, ISBN: 9787300258232) Twenty-five Lectures on Financial Economics. Beijing: China Renmin University Press. (In Chinese)
https://web.stanford.edu/~wfsharpe/apsim/index.html
See Also
Examples
#### an example of Danthine and Donaldson (2005, section 8.3).
uf <- function(x) 0.5 * x[1] + 0.9 * (1 / 3 * log(x[2]) + 2 / 3 * log(x[3]))
ge <- sdm2(
A = function(state) {
VMU <- marginal_utility(state$last.A %*% dg(state$last.z), diag(3), uf, state$p)
Ratio <- sweep(VMU, 2, colMeans(VMU), "/")
A <- state$last.A * Ratio
prop.table(A, 2)
},
B = matrix(0, 3, 2),
S0Exg = matrix(c(
10, 5,
1, 4,
2, 6
), 3, 2, TRUE),
names.commodity = c("asset1", "asset2", "asset3"),
names.agent = c("agt1", "agt2"),
numeraire = "asset1",
ts = TRUE
)
ge$p
#### an example of Sharpe (2008, chapter 2)
asset1 <- c(1, 0, 0, 0, 0)
asset2 <- c(0, 1, 1, 1, 1)
asset3 <- c(0, 5, 3, 8, 4) - 3 * asset2
asset4 <- c(0, 3, 5, 4, 8) - 3 * asset2
# unit asset payoff matrix
UAP <- cbind(asset1, asset2, asset3, asset4)
prob <- c(0.15, 0.25, 0.25, 0.35)
wt <- prop.table(c(1, 0.96 * prob)) # weights
gamma.agt1 <- 1.5
gamma.agt2 <- 2.5
ge <- sdm2(
A = function(state) {
Payoff <- UAP %*% (state$last.A %*% dg(state$last.z))
VMU <- marginal_utility(Payoff, UAP, list(
function(x) CES(alpha = 1, beta = wt, x = x, es = 1 / gamma.agt1),
function(x) CES(alpha = 1, beta = wt, x = x, es = 1 / gamma.agt2)
), price = state$p)
Ratio <- sweep(VMU, 2, colMeans(VMU), "/")
A <- state$last.A * ratio_adjust(Ratio, coef = 0.05, method = "linear")
A <- prop.table(A, 2)
},
B = matrix(0, 4, 2),
S0Exg = matrix(c(
49, 49,
30, 30,
10, 0,
0, 10
), 4, 2, TRUE),
names.commodity = c("asset1", "asset2", "asset3", "asset4"),
names.agent = c("agt1", "agt2"),
numeraire = "asset1"
)
ge$p
ge$p[3:4] + 3 * ge$p[2]
#### an example of Xu (2018, section 10.4, P151)
asset1 <- c(1, 0, 0)
asset2 <- c(0, 1, 0)
asset3 <- c(0, 0, 1)
prob <- c(0.5, 0.5)
wt <- c(1, prob)
UAP <- cbind(asset1, asset2, asset3)
gamma.agt1 <- 1
gamma.agt2 <- 0.5
ge <- sdm2(
A = function(state) {
Payoff <- UAP %*% (state$last.A %*% dg(state$last.z))
VMU <- marginal_utility(Payoff, UAP, list(
# Here CRRA(...)$u, CRRA(...)$CE and CES functions are interexchangeable.
function(x) CRRA(x, gamma = gamma.agt1, p = wt)$u,
function(x) CES(alpha = 1, beta = wt, x = x, es = 1 / gamma.agt2)
), state$p)
Ratio <- sweep(VMU, 2, colMeans(VMU), "/")
A <- state$last.A * Ratio
prop.table(A, 2)
},
B = matrix(0, 3, 2),
S0Exg = matrix(c(
1, 0,
0, 0.5,
0, 2
), 3, 2, TRUE),
names.commodity = c("asset1", "asset2", "asset3"),
names.agent = c("agt1", "agt2"),
numeraire = "asset1",
maxIteration = 1,
ts = TRUE
)
ge$p #c(1, (1 + sqrt(5)) / 4, (1 + sqrt(17)) / 16)
## the same as above.
dst.agt1 <- node_new("util",
type = "CD", alpha = 1, beta = c(0.5, 0.25, 0.25),
"asset1", "asset2", "asset3"
)
dst.agt2 <- node_new("util",
type = "CES", alpha = 1, beta = c(2, 1, 1), sigma = 0.5,
"asset1", "asset2", "asset3"
)
ge <- sdm2(
A = list(dst.agt1, dst.agt2),
B = matrix(0, 3, 2),
S0Exg = matrix(c(
1, 0,
0, 0.5,
0, 2
), 3, 2, TRUE),
names.commodity = c("asset1", "asset2", "asset3"),
names.agent = c("agt1", "agt2"),
numeraire = "asset1",
maxIteration = 1,
ts = TRUE
)
ge$p
#### an example with production.
asset1 <- c(1, 0, 0, 0, 0, 0)
asset2 <- c(0, 1, 0, 0, 0, 0)
asset3 <- c(0, 0, 1, 3, 1, 2)
asset4 <- c(0, 0, 4, 2, 6, 2)
asset5 <- c(0, 0, 1, 0, 2, 0)
# unit asset payoff matrix
UAP <- cbind(asset1, asset2, asset3, asset4, asset5)
muf1 <- function(x) 1 / x
muf2 <- function(x) 1 / x * c(0.4, 0.1, 0.2, 0.05, 0.2, 0.05)
ge <- sdm2(
A = function(state) {
Payoff <- UAP %*% (state$last.A[, 1:2] %*% dg(state$last.z[1:2]))
VMU <- marginal_utility(Payoff, UAP, muf = list(muf1, muf2), price = state$p)
Ratio <- sweep(VMU, 2, colMeans(VMU), "/")
A <- state$last.A[, 1:2] * ratio_adjust(Ratio, coef = 0.15, method = "linear")
A <- prop.table(A, 2)
a.firm <- CD_A(alpha = 4, Beta = c(0.5, 0.5, 0, 0, 0), state$p)
A <- cbind(A, a.firm)
},
B = matrix(c(
0, 0, 0,
0, 0, 0,
0, 0, 0,
0, 0, 0,
0, 0, 1
), 5, 3, TRUE),
S0Exg = matrix(c(
1, 1, NA,
1, 2, NA,
1, NA, NA,
NA, 1, NA,
NA, NA, NA
), 5, 3, TRUE),
names.commodity = c("asset1", "asset2", "asset3", "asset4", "asset5"),
names.agent = c("consumer1", "consumer2", "firm"),
numeraire = "asset1"
)
ge$p
ge$z
#### an example with demand structure trees.
asset1 <- c(1, 0, 0, 0, 0)
asset2 <- c(0, 1, 3, 1, 2)
asset3 <- c(0, 2, 1, 3, 1)
# the asset unit payoff matrix.
UAP <- cbind(asset1, asset2, asset3)
dst.consumer1 <- node_new("util",
type = "CES", es = 0.5, alpha = 1, beta = c(0.5, 0.5),
"x1", "u2"
)
node_set(dst.consumer1, "u2",
type = "CES", es = 0.8, alpha = 1, beta = c(0.6, 0.4),
"u2.1", "u2.2"
)
node_set(dst.consumer1, "u2.1",
type = "CES", es = 1, alpha = 1, beta = c(0.8, 0.2),
"x2", "x3"
)
node_set(dst.consumer1, "u2.2",
type = "CES", es = 1, alpha = 1, beta = c(0.8, 0.2),
"x4", "x5"
)
dst.consumer2 <- node_new("util",
type = "CES", es = 0.5, alpha = 1, beta = c(0.5, 0.5),
"x1", "u2"
)
node_set(dst.consumer2, "u2",
type = "CES", es = 0.8, alpha = 1, beta = c(0.6, 0.4),
"u2.1", "u2.2"
)
node_set(dst.consumer2, "u2.1",
type = "CES", es = 1, alpha = 1, beta = c(0.2, 0.8),
"x2", "x3"
)
node_set(dst.consumer2, "u2.2",
type = "CES", es = 1, alpha = 1, beta = c(0.2, 0.8),
"x4", "x5"
)
uf1 <- function(x) {
names(x) <- paste0("x", seq_along(x))
output(dst.consumer1, x)
}
uf2 <- function(x) {
names(x) <- paste0("x", seq_along(x))
output(dst.consumer2, x)
}
ge <- gemAssetPricing_CUF(
S = matrix(c(
3, 3,
1, 0,
0, 2
), 3, 2, TRUE),
UAP = UAP,
uf = list(uf1, uf2)
)
ge$p
ge$z
[Package GE version 0.4.5 Index]