# Fit Black-Scholes Parameters Over Rolling Window Function to estimate the volatility, $\sigma$, and drift, $\mu$. E.g., the window can be over a given number of months. See `vignette("Distance-to-default", package = "DtD")` for details. ```r 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 $\sigma$. - `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. - `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. ## Returns 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`. ## Examples ```r # 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"]) ``` ## See Also `BS_fit`

BS_fit_rolling function