BS_fit {DtD}

Fit Black-Scholes Parameters

Description

Function to estimate the volatility, \sigma, and drift, \mu. See vignette("Distance-to-default", package = "DtD") for details. All vectors with length greater than one needs to have the same length. The Nelder-Mead method from optim is used when method = "mle". Either time or dt should be passed.

Usage

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

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 \sigma.

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.

Value

A list with the following components

ests

estimates of \sigma, and drift, \mu.

n_iter

number of iterations when method = "iterative" and number of log likelihood evaluations when method = "mle".

success

logical for whether the estimation method converged.

Warning

Choosing tol >= eps or roughly equal may make the method alternate between two solutions for some data sets.

Examples

library(DtD)
set.seed(83486778)
sims <- BS_sim(
  vol = .1, mu = .05, dt = .1, V_0 = 100, T. = 1, D = rep(80, 20), r = .01)

with(sims,
     BS_fit(S = S, D = D, T. = T, r = r, time = time, method = "mle"))