In AnthonyTedde/StockPriceSimulator: Stock Price Simulator

StockPriceSimulator

Introduction

This package provide a way to simulate a fully random stock ticker based on theory provided by "Stochastic Calculus For Finance ii", Shreve"

Functions provided by the package

Key functions

• Stock price generator for a single instance: sstock()
• Stock price generator for a single instance, using the Ito's formula approximation sstock_ito()
• Position taken in hedging strategy: delta()
• First derivative of option pricing function with respect to time: theta()
• Second derivative of option pricing function with respect to stock price: gamma()

Optionals or peripherals functions

• Multiplier used several time: d

Description of the functions as they was created and defined

sstock()

Summary

It returns a data.frame containing the following variables:

• time_periods
• stock_price_path

Arguments

| Arguments | Default | Description | |---|---|---| | time_to_maturity | 4 | Final time up to the Stock Price Path goes | | seed | 1 | It fixes initial value of the pseudo random number generation in order to get reproducible experiments. | | scale | 100 | Define the partition of the time period. | | sigma | 1 | |

Example of Usage

library(StockPriceSimulator)
stock_tick <- sstock()

ggplot2::ggplot(stock_tick, 
                ggplot2::aes(time_periods, stock_price_path)) +
  ggplot2::geom_point()

sstock\ito()

Summary

It returns a data.frame containing the following variables:

• time_periods
• stock_price_path

The computed path is based on approximation given by the Itô's formula.

Arguments

| Arguments | Default | Description | |---|---|---| | time_to_maturity | 4 | Final time up to the Stock Price Path goes | | seed | 1 | It fixes initial value of the pseudo random number generation in order to get reproducible experiments. | | scale | 100 | Define the partition of the time period. | | sigma | 1 | standard deviation of the stock | | alpha | 0 | Mean trend

Example of Usage

library(StockPriceSimulator)
## Call the path generating function from equation:
stock_tick <- sstock(scale = 1000)
## Call the path generating function from Itôs approximation
stock_tick_ito <- sstock_ito(scale = 1000)

ggplot2::ggplot(stock_tick, 
                ggplot2::aes(time_periods, stock_price_path)) +
    ggplot2::geom_point(color = 'pink') +
        ggplot2::geom_line(data = stock_tick_ito,
                           ggplot2::aes(time_periods, stock_price_path),
                           color = 'steelblue')

delta()

Delta return the position one should take in order to hedge a short position in a call.

theta()

gamma()

Test Black-Scholes-Merton function

# Create a stoch price motion from 0 to 4(Year) with a daily step
S <- sstock(initial_stock_price = 50,
            time_to_maturity = 4,
            scale = 360)
# According to the previous sampled path, the option price is computed
# With option in the money
C <- BSM(stock_path = S)

```{R echo=FALSE} ggplot2::ggplot(S, ggplot2::aes(time_periods, stock_price_path)) + ggplot2::geom_point()

```{R echo=FALSE}
ggplot2::ggplot(C, ggplot2::aes(time_periods, option_price_path)) +
  ggplot2::geom_point()

AnthonyTedde/StockPriceSimulator documentation built on May 17, 2019, 5:39 p.m.