---
title: "yrnd_functions"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{yrnd_functions}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(yrnd)
```

```{r setup}
library(yrnd)
```

## yrnd

The package '"yrnd"' estimates a parametric form of the risk neutral distribution of prices of fixed-income futures such as Short Term Interest Rates futures and sovereign bond futures, using options written on those futures. The horizon of the fitted rnd is at option's maturity. The package also provides with the distribution of STIR rates and sovereign bond yields themselves at options' maturity, starting from the density of the futures price. It provides with some statistics of the distribution as well as a density and a cumulative density plot.

## ctd_bond_yield provides with the risk neutral density of the yield to maturity of the Cheapest-to-Deliver Bond in a futures contract, using options on the government bond future

```{r}
ctd_bond_yield(c(10.39,9.92,9.46,9.00,8.55,8.10,7.66,7.23,
6.81,6.39,5.98,5.58,5.20,4.82,4.46,4.10,3.76,3.44,3.13,2.83,2.56,
2.29,2.05,1.82,1.61,1.42,1.25,1.09,0.95,0.82,0.71,0.61,0.53,0.45,
0.38,0.33,0.28,0.23,0.20,0.17,0.14,0.12,0.10,0.08),
seq(106, 127.5, 0.5),
c(0.22,0.25,0.29,0.33,0.38,0.43,0.49,0.56,0.64,0.72,0.81,0.91,
1.03,1.15,1.29, 1.43,1.59,1.77,1.96,2.16,2.39,2.62,2.88,3.15,
3.44,3.75,4.08, 4.42,4.78,5.15,5.54,5.94,6.36,6.78,7.21,7.66,
8.11,8.56,9.03, 9.50,9.97,10.45,10.93,11.41),
seq(106, 127.5, 0.5),
2,
0.0344,
0.035,
1,
3,
0.893,
0.0435, 
as.Date("2033-11-01"),
0.5,
100,
2,
116.17,
as.Date("2024-12-10"),
as.Date("2024-11-22"),
as.Date("2024-06-14"),
"Italian",
"EUR")
```


## bond_future_price provides with the risk neutral density of the government bond futures price, using options on the government bond future

```{r}
bond_future_price(c(10.39,9.92,9.46,9.00,8.55,8.10,7.66,7.23,
6.81,6.39,5.98,5.58,5.20,4.82,4.46,4.10,3.76,3.44,3.13,2.83,2.56,
2.29,2.05,1.82,1.61,1.42,1.25,1.09,0.95,0.82,0.71,0.61,0.53,0.45,
0.38,0.33,0.28,0.23,0.20,0.17,0.14,0.12,0.10,0.08),
seq(106, 127.5, 0.5),
c(0.22,0.25,0.29,0.33,0.38,0.43,0.49,0.56,0.64,0.72,0.81,0.91,
1.03,1.15,1.29, 1.43,1.59,1.77,1.96,2.16,2.39,2.62,2.88,3.15,
3.44,3.75,4.08, 4.42,4.78,5.15,5.54,5.94,6.36,6.78,7.21,7.66,
8.11,8.56,9.03, 9.50,9.97,10.45,10.93,11.41),
seq(106, 127.5, 0.5),
2,
0.0344,
1,
3,
as.Date("2033-11-01"),
116.17,
as.Date("2024-12-10"),
as.Date("2024-11-22"),
as.Date("2024-06-14"),
"Italian",
"EUR")
```


## stir_future_price provides with the risk neutral density of the STIR futures price, using options on the STIR future

```{r}
stir_future_price( c(1.44500, 1.32000, 1.19750, 1.07500, 0.95750,
0.84250, 0.78750, 0.73250, 0.68000, 0.62750, 0.57750, 0.53000, 0.48500,
0.44000, 0.39750, 0.35750, 0.32000, 0.28500, 0.25250, 0.22250, 0.19500,
0.17000, 0.14750, 0.12750, 0.10750, 0.09250, 0.07750, 0.06500, 0.05500,
0.04500, 0.03750, 0.03000, 0.02500, 0.02000, 0.01500, 0.01250, 0.01000,
0.00750, 0.00500, 0.00500, 0.00250, 0.00250, 0.00250, 0.00250,
rep(0.00024, 47)),
c(seq(93.25, 93.875, 0.125),  seq(93.9375, 98.8125, 0.0625),
seq(98.875, 99.5, 0.125)),
c(0.0025, 0.0050, 0.0075, 0.0125, 0.0175, 0.0300, 0.0350, 0.0425, 0.0525,
0.0625, 0.0750, 0.0900, 0.1050, 0.1225, 0.1425, 0.1650, 0.1900, 0.2175,
0.2450, 0.2775, 0.3125, 0.3500, 0.3875, 0.4300, 0.4725, 0.5175, 0.5675,
0.6150, 0.6675, 0.7200, 0.7750, 0.8300, 0.8850, 0.9425, 1.0025, 1.0625,
1.1225, 1.1825, 1.2425, 1.3050, 1.3675, 1.4300, 1.4925, 1.5550, 1.6175,
1.6800, 1.7425, 1.8050, 1.8675, 1.9300, 1.9925, 2.0550, 2.1175, 2.1800,
2.2425, 2.3050, 2.3675, 2.4300, 2.4925, 2.5550, 2.6175, 2.6800, 2.7425,
2.8050, 2.8675, 2.9300, 2.9925, 3.0550, 3.1175, 3.1800, 3.2425, 3.3050,
3.3675, 3.4300, 3.4925, 3.5550, 3.6175, 3.6800, 3.7425, 3.8050, 3.8675,
3.9300, 3.9925, 4.0550, 4.1175, 4.1800, 4.3050, 4.4300, 4.5550, 4.6800,
4.8050),
c(seq(93.25, 93.875, 0.125),  seq(93.9375, 98.8125, 0.0625),
seq(98.875, 99.5, 0.125)),
2,
0.0537,
1,
3,
94.7,
as.Date("2024-02-29"),
as.Date("2024-02-25"),
as.Date("2023-12-18"),
"fed_fund_rate",
"USD")
```

## stir_rate provides with the risk neutral density of the STIR rate implicit in the STIR futures price, using options on the STIR future

```{r}
stir_rate( c(1.44500, 1.32000, 1.19750, 1.07500, 0.95750,
0.84250, 0.78750, 0.73250, 0.68000, 0.62750, 0.57750, 0.53000, 0.48500,
0.44000, 0.39750, 0.35750, 0.32000, 0.28500, 0.25250, 0.22250, 0.19500,
0.17000, 0.14750, 0.12750, 0.10750, 0.09250, 0.07750, 0.06500, 0.05500,
0.04500, 0.03750, 0.03000, 0.02500, 0.02000, 0.01500, 0.01250, 0.01000,
0.00750, 0.00500, 0.00500, 0.00250, 0.00250, 0.00250, 0.00250,
rep(0.00024, 47)),
c(seq(93.25, 93.875, 0.125),  seq(93.9375, 98.8125, 0.0625),
seq(98.875, 99.5, 0.125)),
c(0.0025, 0.0050, 0.0075, 0.0125, 0.0175, 0.0300, 0.0350, 0.0425,
0.0525, 0.0625, 0.0750, 0.0900, 0.1050, 0.1225, 0.1425, 0.1650, 0.1900,
0.2175, 0.2450, 0.2775, 0.3125, 0.3500, 0.3875, 0.4300, 0.4725, 0.5175,
0.5675, 0.6150, 0.6675, 0.7200, 0.7750, 0.8300, 0.8850, 0.9425, 1.0025,
1.0625, 1.1225, 1.1825, 1.2425, 1.3050, 1.3675, 1.4300, 1.4925, 1.5550,
1.6175, 1.6800, 1.7425, 1.8050, 1.8675, 1.9300, 1.9925, 2.0550, 2.1175,
2.1800, 2.2425, 2.3050, 2.3675, 2.4300, 2.4925, 2.5550, 2.6175, 2.6800,
2.7425, 2.8050, 2.8675, 2.9300, 2.9925, 3.0550, 3.1175, 3.1800, 3.2425,
3.3050, 3.3675, 3.4300, 3.4925, 3.5550, 3.6175, 3.6800, 3.7425, 3.8050,
3.8675, 3.9300, 3.9925, 4.0550, 4.1175, 4.1800, 4.3050, 4.4300, 4.5550,
4.6800, 4.8050),
c(seq(93.25, 93.875, 0.125),  seq(93.9375, 98.8125, 0.0625),
seq(98.875, 99.5, 0.125)),
2,
0.0537,
1,
3,
94.7,
as.Date("2024-02-29"),
as.Date("2024-02-25"),
as.Date("2023-12-18"),
"fed_fund_rate",
"USD")
```