merton_ll: Compute Log-Likelihood of Merton Model

In DtD: Distance to Default

Description

Computes the log-likelihood for a given values of μ and σ.

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 σ value.
mu	numeric scalar with the μ 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)))

DtD documentation built on March 26, 2020, 7:45 p.m.