ragtop

R-CMD-check CRAN status

ragtop prices equity derivatives using variants of the famous Black-Scholes model, with special attention paid to the case of American and European exercise options and to convertible bonds.

Installation

You can install the released version of ragtop from CRAN with:

install.packages("ragtop")

And the development version from GitHub with:

# install.packages("pak")
pak::pak("brianboonstra/ragtop")

Usage

Basic Usage

You can price american and european exercise options, either individually, or in groups. In the simplest case that looks like this for European exercise

blackscholes(c(CALL, PUT), S0 = 100, K = c(100, 110), time = 0.77, r = 0.06, vola = 0.20)
#> $Price
#> [1] 9.326839 9.963285
#> 
#> $Delta
#> [1]  0.6372053 -0.5761608
#> 
#> $Vega
#> [1] 32.91568 34.36717

and like this for American exercise

american(PUT, S0 = 100, K = c(100, 110), time = 0.77, const_short_rate = 0.06, const_volatility = 0.20)
#> A100_281_0 A110_281_0 
#>    5.24386   11.27715

Including Term Structures

There are zillions of implementations of the Black-Scholes formula out there, and quite a few simple trees as well. One thing that makes ragtop a bit more useful than most other packages is that it treats dividends and term structures without too much pain. Assume we have some nontrivial term structures and dividends

## Dividends
divs = data.frame(time = seq(from = 0.11, to = 2, by = 0.25),
                  fixed = seq(1.5, 1, length.out = 8),
                  proportional = seq(1, 1.5, length.out = 8))

## Interest rates
disct_fcn = ragtop::spot_to_df_fcn(data.frame(time = c(1, 5, 10),
                                              rate = c(0.01, 0.02, 0.035)))

## Default intensity
disc_factor_fcn = function(T, t, ...) {
  exp(-0.03 * (T - t)) }
surv_prob_fcn = function(T, t, ...) {
  exp(-0.07 * (T - t)) }

## Variance cumulation / volatility term structure
vc = variance_cumulation_from_vols(
   data.frame(time = c(0.1, 2, 3),
              volatility = c(0.2, 0.5, 1.2)))
paste0("Cumulated variance to 18 months is ", vc(1.5, 0))
#> [1] "Cumulated variance to 18 months is 0.369473684210526"

then we can price vanilla options

black_scholes_on_term_structures(
   callput = TSLAMarket$options[500, 'callput'],
   S0 = TSLAMarket$S0,
   K = TSLAMarket$options[500, 'K'],
   discount_factor_fcn = disct_fcn,
   time = TSLAMarket$options[500,'time'],
   variance_cumulation_fcn = vc,
   dividends = divs)
#> $Price
#> [1] 62.55998
#> 
#> $Delta
#> [1] 0.7977684
#> 
#> $Vega
#> [1] 52.21925

American exercise options

american(
    callput = TSLAMarket$options[400, 'callput'],
    S0 = TSLAMarket$S0,
    K = TSLAMarket$options[400, 'K'],
    discount_factor_fcn = disct_fcn,
    time = TSLAMarket$options[400, 'time'],
    survival_probability_fcn = surv_prob_fcn,
    variance_cumulation_fcn = vc,
    dividends = divs)
#> A360_137_2 
#>   2.894296

We can also find volatilities of European exercise options

implied_volatility_with_term_struct(
    option_price = 19, callput = PUT,
    S0 = 185.17, K = 182.50,
    discount_factor_fcn = disct_fcn,
    time = 1.12,
    survival_probability_fcn = surv_prob_fcn,
    dividends = divs)
#> [1] 0.1133976

as well as American exercise options

american_implied_volatility(
    option_price = 19, callput = PUT,
    S0 = 185.17, K = 182.50,
    discount_factor_fcn = disct_fcn,
    time = 1.12,
    survival_probability_fcn = surv_prob_fcn,
    dividends = divs)
#> [1] 0.113407

More Sophisticated Calibration

You can also find more complete calibration routines in ragtop. See the vignette or the documentation for fit_variance_cumulation and fit_to_option_market.

Technical Documentation

The source for the technical paper is in this repository. You can also find the pdf here