{"id":3510,"date":"2019-05-15T11:28:23","date_gmt":"2019-05-15T15:28:23","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=3510"},"modified":"2025-02-07T15:08:14","modified_gmt":"2025-02-07T20:08:14","slug":"real-world-tidy-interest-rate-swap-pricing","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/real-world-tidy-interest-rate-swap-pricing\/","title":{"rendered":"Real world tidy interest rate swap pricing"},"content":{"rendered":"\n

In this post I will show how easy it is to price a portfolio of swaps leveraging the purrr<\/strong> package and given the swap pricing functions that we introduced in a previous post<\/a>. I will do this in a \u201creal world\u201d environment using real market data from April 14.<\/p>\n\n\n\n

Import the discount factors from Bloomberg<\/p>\n\n\n\n

Let\u2019s start the pricing of the swap portfolio with\u00a0purrr<\/strong>\u00a0by loading from an external source the EUR discount factor curve. My source is\u00a0Bloomberg,<\/em>\u00a0and in particular the\u00a0SWPM<\/em>\u00a0page, which allows all Bloomberg users to price interest rate sensitive instruments. It also contains a tab with the curve information, which is the source of my curve. It is partly represented in the screenshot below, as well as in the following table:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
today <- lubridate::ymd(20190414)\n ir_curve <- readr::read_csv(here::here(\"data\/Basket of IRS\/Curve at 140419.csv\"))\n ir_curve %>%\n knitr::kable(caption = \"Input from Bloomberg\", \"html\") %>%\n kableExtra::kable_styling(bootstrap_options = c(\"striped\", \"hover\", \"condensed\", \"responsive\")) %>%\n kableExtra::scroll_box(width = \"750px\", height = \"200px\") <\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Note: R code and table can be downloaded from Davide\u2019s website:
https:\/\/www.curiousfrm.com\/2019\/04\/real-world-tidy-interest-rate-swap-pricing\/<\/a><\/em><\/p>\n\n\n\n
We now wrangle this data in order to get a two-column tibble containing the time to maturity and the discount factors for each pillar points on the curve. We us a 30\/360<\/em>-day count convention because it is the standard for the EUR <\/p>\n\n\n\n
df.table <- ir_curve %>%\n\n\tdplyr::mutate(`Maturity Date` = lubridate::mdy(`Maturity Date`)) %>%\n\n\tdplyr::rowwise(.) %>%\n\n\tdplyr::mutate(t2m = RQuantLib::yearFraction(today, `Maturity Date`, 6)) %>%\n\n\tna.omit %>%\n\n\tdplyr::select(t2m, Discount) %>%\n\n\tdplyr::rename(df = Discount) %>%\n\n\tdplyr::ungroup(.) %>%\n\n\tdplyr::bind_rows(c(t2m = 0,df = 1)) %>%\n\n\tdplyr::arrange(t2m)\n\n\t\n\n\tggplot2::ggplot(df.table, ggplot2::aes(x = t2m, y = df)) +\n\n\tggplot2::geom_point() + ggplot2::geom_line(colour = \"blue\") +\n\n\tggplot2::ggtitle(\"Discount Factor curve at 14th of April 2019\") +\n\n\tggplot2::xlab(\"Time to maturity\") +\n\n\tggplot2::ylab(\"Discount Factor\")\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Interest Rate Swap pricing functions<\/strong><\/p>\n\n\n\n
I am now going to re-use the pricing functions that have been already described in a previous post<\/a>. I have tidied them up a bit and given proper names, but the description still fully holds.<\/p>\n\n\n\n
 Let\u2019s start from the one that calculates the swap cashflows. <\/p>\n\n\n\n
SwapCashflowYFCalculation <- function(today, start.date, maturity.date,\n\n\ttime.unit, dcc, calendar) { \n0:((lubridate::year(maturity.date) - lubridate::year(start.date)) *\n\n\t(4 - time.unit)) %>%\n\n\tpurrr::map_dbl(~RQuantLib::advance(calendar = calendar,\n\n\tdates = start.date,\n\n\tn = .x, timeUnit = time.unit,\n\n\tbdc = 1,\n\n\temr = TRUE)) %>%\n\n\tlubridate::as_date() %>% {\n\nif (start.date < today) append(today, .) else .} %>%\n\n\tpurrr::map_dbl(~RQuantLib::yearFraction(today, .x, dcc)) %>%\n\n\ttibble::tibble(yf = .) }<\/code><\/pre>\n\n\n\n
<\/p>\n\n\n\n
You may have noticed that I added one row {if (start.date < today) append(today, .) else .}<\/code>. This allows  proper management of the pricing of swaps with a starting date before today.<\/p>\n\n\n\n
I now proceed with calculating the actual par swap rate, which is a key input to the pricing formula. Notice in the function below that I use a linear interpolation on the log of the discount factors. This is in line with one of the Bloomberg options. It is proven that it:<\/p>\n\n\n\n
    \n
  1. provides step constant forward rates<\/li>\n\n\n\n
  2. locally stabilizes the bucketed sensitivities<\/li>\n<\/ol>\n\n\n\n
    Also, the (old) swap rate pricing function is the same. We only filter for future cashflows, as we want to be able to price swaps with a starting date before today. <\/p>\n\n\n\n
    OLDParSwapRate <- function(swap.cf){\n swap.cf %<>%\n dplyr::filter(yf >= 0)\n\n num <- (swap.cf$df[1] - swap.cf$df[dim(swap.cf)[1]])\n\n annuity <- (sum(diff(swap.cf$yf)*swap.cf$df[2:dim(swap.cf)[1]])) \nreturn(list(swap.rate = num\/annuity,\n annuity = annuity))\n\n }\n\n ParSwapRateCalculation <- function(\n swap.cf.yf, df.table) { swap.cf.yf %>%\n dplyr::mutate(df = approx(df.table$t2m, log(df.table$df), .$yf) %>%\n purrr::pluck(\"y\") %>%\n exp) %>%\n OLDParSwapRate\n }<\/code><\/pre>\n\n\n\n
    I now want to introduce two new functions which are needed for calculating the actual market values:<\/p>\n\n\n\n