Movatterモバイル変換

European Call Option Price and the Inverse

Description

Computes the European call option and the inverse. All vectorswith length greater than one needs to have the same length.

Usage

BS_call(V, D, T., r, vol)get_underlying(S, D, T., r, vol, tol = 1e-12)

Arguments

Value

Numeric vector or scalar with price of the underlying asset or equity price.

See Also

BS_fit

Examples

library(DtD)set.seed(58661382)sims <- BS_sim(  vol = .2, mu = .03, dt = .1, V_0 = 100, T. = 1, D = rep(80, 20), r = .01)stopifnot(with(  sims, isTRUE(all.equal(V, get_underlying(S, D, T, r, vol)))))stopifnot(with(  sims, isTRUE(all.equal(S, BS_call(V, D, T, r, vol)))))

Fit Black-Scholes Parameters

Description

Function to estimate the volatility,\sigma, and drift,\mu. Seevignette("Distance-to-default", package = "DtD") for details. Allvectors with length greater than one needs to have the same length. TheNelder-Mead method fromoptim is used whenmethod = "mle". Eithertime ordt 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

Value

A list with the following components

Warning

Choosingtol >= eps or roughly equal may make the method alternatebetween 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"))

Fit Black-Scholes Parameters Over Rolling Window

Description

Function to estimate the volatility,\sigma, and drift,\mu. E.g.,the window can be over a given number of months. Seevignette("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

Value

Matrix with thegrp, number of observation in the window, parameterestimates, and'n_iter' as inBS_fit, and whether theestimation method was successful.

Anerror attribute is added in case other code thanoptim fails. It is a list of lists with thegrp indexwhere the method failed and the output fromtry.

See Also

BS_fit

Examples

# Simulate dataset.seed(55770945)n <- 21L * 3L * 12L # 21 trading days for 3 years w/ 12 monthssims <- BS_sim(  vol = .1, mu = .05, dt = .1, V_0 = 100, T. = 1,  D = runif(n, 80, 90), r = runif(n, 0, .01))sims$month <- (1:nrow(sims) - 1L) %/% 21L + 1L# throw out some monthssims <- subset(sims, !month %in% 15:24)# assign parametersgrp <- sims$monthwidth <- 12L        # window w/ 12 month widthmin_obs <- 21L * 3L # require 3 months of data# estimate results with R loop which is slightly simpler then the# implementationgrps <- 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 functionout_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"])

Simulate Stock Price and Price of Underlying Asset

Description

At least one ofD,r, orT. needs to havethe desired length of the simulated series. All vectors with length greaterthan one needs to have the same length.

Usage

BS_sim(vol, mu, dt, V_0, D, r, T.)

Arguments

See Also

BS_fit

Examples

library(DtD)set.seed(79156879)sims <- BS_sim(  vol = .1, mu = .05, dt = .2, V_0 = 100, T. = 1, D = rep(80, 20), r = .01)# plot underlyingplot(sims$V)# plot stockplot(sims$S)

Compute Log-Likelihood of Merton Model

Description

Computes the log-likelihood for a given values of\mu and\sigma.

Usage

merton_ll(S, D, T., r, time, dt, vol, mu, tol = 1e-12)

Arguments

See Also

BS_fit

Examples

# we get the same if we call `optim` as follows. The former is faster and is# recommendedset.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 thisll <- 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)))