BS_fit_rolling: Fit Black-Scholes Parameters Over Rolling Window

In DtD: Distance to Default

Description

Function to estimate the volatility, σ, and drift, μ. E.g., the window can be over a given number of months. See vignette("Distance-to-default", package = "DtD") for details.

Usage

BS_fit_rolling(
  S,
  D,
  T.,
  r,
  time,
  dt,
  vol_start,
  method = c("iterative", "mle"),
  tol = 1e-12,
  eps = 1e-08,
  grp,
  width,
  min_obs
)

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_start	numeric scalar with starting value for σ.
method	string to specify which estimation method to use.
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.
eps	numeric scalar with convergence threshold.
grp	integer vector with the group identifier (e.g., units of months).
width	integer scalar with the units of grp to include in the rolling window.
min_obs	integer scalar for the minimum number of observation required in each window.

Value

Matrix with the grp, number of observation in the window, parameter estimates, and 'n_iter' as in BS_fit, and whether the estimation method was successful.

An error attribute is added in case other code than optim fails. It is a list of lists with the grp index where the method failed and the output from try.

See Also

BS_fit

Examples

# Simulate data
set.seed(55770945)
n <- 21L * 3L * 12L # 21 trading days for 3 years w/ 12 months
sims <- BS_sim(
  vol = .1, mu = .05, dt = .1, V_0 = 100, T. = 1,
  D = runif(n, 80, 90), r = runif(n, 0, .01))
sims$month <- (1:nrow(sims) - 1L) %/% 21L + 1L

# throw out some months
sims <- subset(sims, !month %in% 15:24)

# assign parameters
grp <- sims$month
width <- 12L        # window w/ 12 month width
min_obs <- 21L * 3L # require 3 months of data

# estimate results with R loop which is slightly simpler then the
# implementation
grps <- unique(grp)
out <- matrix(
  NA_real_, nrow = length(grps), ncol = 6,
  dimnames = list(NULL, c("mu", "vol", "n_iter", "success", "n_obs", "grp")))
for(g in grps){
  idx <- which(grps == g)
  keep <- which(grp %in% (g - width + 1L):g)
  out[idx, c("n_obs", "grp")] <- c(length(keep), g)
  if(length(keep) < min_obs)
    next
  res <- with(
    sims[keep, ],
    BS_fit(S = S, D = D, T. = T, r = r, time = time, method = "iterative",
           vol_start = 1))
  out[idx, c("mu", "vol", "n_iter", "success")] <- rep(
    do.call(c, res[c("ests", "n_iter", "success")]), each = length(idx))
}

# we get the same with the R function
out_func <- with(sims, BS_fit_rolling(
  S = S, D = D, T. = T, r = r, time = time, method = "iterative",
  grp = month, width = width, min_obs = min_obs))

all.equal(out[, names(out) != "n_iter"],
          out_func[, names(out_func) != "n_iter"])

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