**ragtop** prices equity derivatives are priced on variants of the famous Black-Scholes model, with special attention paid to the case of American and European exercise options and to convertible bonds. To install the development version, use the command

`devtools::install_github('brianboonstra/ragtop')`

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
```

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
```

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*.

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