# BS_fit

0th

Percentile

##### Fit Black-Scholes Parameters

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.

• BS_fit
##### Examples
# NOT RUN {
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"))

# }

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

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