Whytvm?

Well, first,tvm stands for “time value of money”, theusual name for financial calculations that involve interest rates,present values and future values.

Base R doesn’t have built-in calculations for this, and they are onof the most used functions in Excel for financial calculations.tvm attempts to provide these calculations to the user,using known Excel names where possible.

Simple present values and rate calculations

For the Excel user, the following functions will be known

• npv
• xpnv
• irr
• xirr
• pmt
• rate

These work as expected, and require no further explanation. Pleasecheck the documentation or the README for some examples.

Rate curves

A rate curve is an abstraction for a set of rates with differentmaturities. Currently,tvm only supports creating curveswith equally spaced maturities, where the periodicity is implicitlyspecified by the user (i.e., no dates accepted).

In the current implementation, a rate curve is a S3 class, based on alist which has 2 components: a discount factor function $f, and anumeric vector $knots, which corresponds to the points of the curvewhere the bootstrapping between the different rate types is done.

The different rate types used are - zero (spot rates) in effectiveand nominal form (effective are compounded, nominal are linear) - fut(futures rate) - swap (bullet rates) - french (french type loans) -german (german type loans)

You create a rate curve with the constructor, and the use subsettingto get functions for the different loan structures. Note that only somerate types are available in the constructor.

The basis for all the curves are the discount factor. Within theconstructor, calculations are performed to find the discount factorsthat create a curve equivalent to the one given.

You can create rate curves from a vector of rates (it is assumed thatrates[i] is the rate corresponding to theiperiod), a rate function (given a maturity returns a rate) or a discountfunction (given a maturity returns a discount factor)

rate_curve(rates =c(0.1,0.2,0.3),rate_type ="zero_eff")

## $f## function (x, deriv = 0, extrapol = c("linear", "cubic")) ## {##     extrapol <- match.arg(extrapol)##     deriv <- as.integer(deriv)##     if (deriv < 0 || deriv > 3) ##         stop("'deriv' must be between 0 and 3")##     i <- findInterval(x, x0, all.inside = (extrapol == "cubic"))##     if (deriv == 0) ##         interp <- function(x, i) {##             h <- dx[i]##             t <- (x - x0[i])/h##             t1 <- t - 1##             h01 <- t * t * (3 - 2 * t)##             h00 <- 1 - h01##             tt1 <- t * t1##             h10 <- tt1 * t1##             h11 <- tt1 * t##             y0[i] * h00 + h * m[i] * h10 + y0[i + 1] * h01 + ##                 h * m[i + 1] * h11##         }##     else if (deriv == 1) ##         interp <- function(x, i) {##             h <- dx[i]##             t <- (x - x0[i])/h##             t1 <- t - 1##             h01 <- -6 * t * t1##             h10 <- (3 * t - 1) * t1##             h11 <- (3 * t - 2) * t##             (y0[i + 1] - y0[i])/h * h01 + m[i] * h10 + m[i + ##                 1] * h11##         }##     else if (deriv == 2) ##         interp <- function(x, i) {##             h <- dx[i]##             t <- (x - x0[i])/h##             h01 <- 6 * (1 - 2 * t)##             h10 <- 2 * (3 * t - 2)##             h11 <- 2 * (3 * t - 1)##             ((y0[i + 1] - y0[i])/h * h01 + m[i] * h10 + m[i + ##                 1] * h11)/h##         }##     else interp <- function(x, i) {##         h <- dx[i]##         h01 <- -12##         h10 <- 6##         h11 <- 6##         ((y0[i + 1] - y0[i])/h * h01 + m[i] * h10 + m[i + 1] * ##             h11)/h##     }##     if (extrapol == "linear" && any(iXtra <- (iL <- (i == 0)) | ##         (iR <- (i == (n <- length(x0)))))) {##         r <- x##         if (any(iL)) ##             r[iL] <- if (deriv == 0) ##                 y0[1L] + m[1L] * (x[iL] - x0[1L])##             else if (deriv == 1) ##                 m[1L]##             else 0##         if (any(iR)) ##             r[iR] <- if (deriv == 0) ##                 y0[n] + m[n] * (x[iR] - x0[n])##             else if (deriv == 1) ##                 m[n]##             else 0##         ini <- !iXtra##         r[ini] <- interp(x[ini], i[ini])##         r##     }##     else {##         interp(x, i)##     }## }## <bytecode: 0x000001ef4e210d20>## <environment: 0x000001ef4e228b78>## ## $knots## [1] 1 2 3## ## $functor## function (x, y) ## splinefun(x = x, y = y, method = "monoH.FC")## <environment: 0x000001ef4e15a138>## ## $rate_scale## [1] 1## ## attr(,"class")## [1] "rate_curve"

rate_curve(fun_r =function(x)rep_len(0.1,length(x)),rate_type ="swap",knots =1:10)

## $f## function (x, deriv = 0, extrapol = c("linear", "cubic")) ## {##     extrapol <- match.arg(extrapol)##     deriv <- as.integer(deriv)##     if (deriv < 0 || deriv > 3) ##         stop("'deriv' must be between 0 and 3")##     i <- findInterval(x, x0, all.inside = (extrapol == "cubic"))##     if (deriv == 0) ##         interp <- function(x, i) {##             h <- dx[i]##             t <- (x - x0[i])/h##             t1 <- t - 1##             h01 <- t * t * (3 - 2 * t)##             h00 <- 1 - h01##             tt1 <- t * t1##             h10 <- tt1 * t1##             h11 <- tt1 * t##             y0[i] * h00 + h * m[i] * h10 + y0[i + 1] * h01 + ##                 h * m[i + 1] * h11##         }##     else if (deriv == 1) ##         interp <- function(x, i) {##             h <- dx[i]##             t <- (x - x0[i])/h##             t1 <- t - 1##             h01 <- -6 * t * t1##             h10 <- (3 * t - 1) * t1##             h11 <- (3 * t - 2) * t##             (y0[i + 1] - y0[i])/h * h01 + m[i] * h10 + m[i + ##                 1] * h11##         }##     else if (deriv == 2) ##         interp <- function(x, i) {##             h <- dx[i]##             t <- (x - x0[i])/h##             h01 <- 6 * (1 - 2 * t)##             h10 <- 2 * (3 * t - 2)##             h11 <- 2 * (3 * t - 1)##             ((y0[i + 1] - y0[i])/h * h01 + m[i] * h10 + m[i + ##                 1] * h11)/h##         }##     else interp <- function(x, i) {##         h <- dx[i]##         h01 <- -12##         h10 <- 6##         h11 <- 6##         ((y0[i + 1] - y0[i])/h * h01 + m[i] * h10 + m[i + 1] * ##             h11)/h##     }##     if (extrapol == "linear" && any(iXtra <- (iL <- (i == 0)) | ##         (iR <- (i == (n <- length(x0)))))) {##         r <- x##         if (any(iL)) ##             r[iL] <- if (deriv == 0) ##                 y0[1L] + m[1L] * (x[iL] - x0[1L])##             else if (deriv == 1) ##                 m[1L]##             else 0##         if (any(iR)) ##             r[iR] <- if (deriv == 0) ##                 y0[n] + m[n] * (x[iR] - x0[n])##             else if (deriv == 1) ##                 m[n]##             else 0##         ini <- !iXtra##         r[ini] <- interp(x[ini], i[ini])##         r##     }##     else {##         interp(x, i)##     }## }## <bytecode: 0x000001ef4e210d20>## <environment: 0x000001ef4e2d1df8>## ## $knots##  [1]  1  2  3  4  5  6  7  8  9 10## ## $functor## function (x, y) ## splinefun(x = x, y = y, method = "monoH.FC")## <environment: 0x000001ef4e29ea28>## ## $rate_scale## [1] 1## ## attr(,"class")## [1] "rate_curve"

rate_curve(fun_d =function(x)1/ (1+ x),knots =1:10)

## $f## function(x) 1 / (1 + x)## ## $knots##  [1]  1  2  3  4  5  6  7  8  9 10## ## $functor## function (x, y) ## splinefun(x = x, y = y, method = "monoH.FC")## <environment: 0x000001ef4e364df0>## ## $rate_scale## [1] 1## ## attr(,"class")## [1] "rate_curve"

The subset operator allows you to retrieve certain rates only, orretrieve the equivalent rate curve in another type

r<-rate_curve(rates =c(0.1,0.2,0.3),rate_type ="zero_eff")r[,c(1,2)]

## [1] 0.1 0.2

r["zero_eff"]

## function (x) ## rescale(f(x), rate_scale = r$rate_scale, rate_type = rate_type)## <bytecode: 0x000001ef4ec6eb00>## <environment: 0x000001ef4ecfe390>

r["swap",c(1.5,2)]

## [1] 0.1463039 0.1905512

Plotting rate curves is supported, and you can choose which rate typeor types to plot

plot(r)

plot(r,rate_type ="german")

plot(r,rate_type =c("french","german"))