README.Rmd

---
output:
  md_document:
    variant: markdown_github
---
```{r global_options, include=FALSE}
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)

```

<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r, echo = 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

```{r, echo=TRUE}
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

```{r bs, echo=TRUE}
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

```{r bsa, echo=TRUE}
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

```{r ts_fcns, echo=TRUE, comment=""}
## 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

```{r blackscholes_ts, comment="", echo=TRUE}
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

```{r amer_ts, echo=TRUE, comment=""}
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

```{r implied_bs_volatility_def_ts, comment="", echo =T}
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

```{r amer_ts_iv, echo=TRUE, comment=""}
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](http://thureoscapital.com/ragtop.pdf)

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