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-" )
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')
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)
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)
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
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