library(ragtop)
library(futile.logger)
library(ggplot2)

flog.threshold(ERROR)
flog.threshold(ERROR, name='ragtop.implicit.timestep.construct_tridiagonals')
flog.threshold(ERROR, name='ragtop.calibration.implied_volatility.lowprice')
flog.threshold(ERROR, name='ragtop.calibration.implied_volatility_with_term_struct')
flog.threshold(ERROR, name='ragtop.implicit.setup.width')

knitr::opts_chunk$set(fig.width=6.5, fig.height=4, fig.path='Figs/',
                      echo=FALSE, warning=FALSE, message=FALSE, comment=FALSE)
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "README-"
)

Description And Installation

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. To install the development version, use the command

devtools::install_github('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)

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)

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))

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)

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)

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)

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)

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

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brianboonstra/ragtop documentation built on March 7, 2020, 2:23 p.m.