# merton_ll

0th

Percentile

##### Compute Log-Likelihood of Merton Model

Computes the log-likelihood for a given values of $\mu$ and $\sigma$.

##### Usage
merton_ll(S, D, T., r, time, dt, vol, mu, tol = 1e-12)
##### Arguments
S

numeric vector with observed stock prices.

D

numeric vector or scalar with debt due in T..

T.

numeric vector or scalar with time to maturity.

r

numeric vector or scalar with risk free rates.

time

numeric vector with the observation times.

dt

numeric scalar with time increments between observations.

vol

numeric scalar with the $\sigma$ value.

mu

numeric scalar with the $\mu$ value.

tol

numeric scalar with tolerance to get_underlying. The difference is scaled if the absolute of S is large than tol as in the tolerance argument to all.equal.numeric.

BS_fit

• merton_ll
##### Examples
# NOT RUN {
# we get the same if we call optim as follows. The former is faster and is
# recommended
set.seed(4648394)
sims <- BS_sim(
vol = .1, mu = .05, dt = .1, V_0 = 100, T. = 1, D = rep(80, 20), r = .01)

r1 <- with(
sims, BS_fit(S = S, D = D, T. = T, r = r, time = time, method = "mle",
eps = 1e-8, vol_start = .2))

r2 <- optim(c(mu = 0, log_vol = log(.2)), function(par)
-with(
sims, merton_ll(S = S, D = D, T. = T, r = r, time = time,
mu = par["mu"], vol = exp(par["log_vol"]))))

all.equal(r1$n_iter, unname(r2$counts[1]))
all.equal(r1$ests[1], r2$par[1])
all.equal(r1$ests[2], exp(r2$par[2]), check.attributes = FALSE)

# the log-likelihood integrates to one as it should though likely not the
# most stable way to test this
ll <- integrate(
function(x) sapply(x, function(S)
exp(merton_ll(
S = c(1, S), D = .8, T. = 3, r = .01, dt = 1/250, vol = .2,
mu = .05))),
lower = 1e-4, upper = 6)
stopifnot(isTRUE(all.equal(ll\$value, 1, tolerance = 1e-5)))

# }

Documentation reproduced from package DtD, version 0.2.1, License: GPL-2

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