merton_ll {DtD}

Compute Log-Likelihood of Merton Model

Description

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.

See Also

BS_fit

Examples

# 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)))