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AnthonyTedde / StockPriceSimulator

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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)

##
## Attaching package: 'StockPriceSimulator'

## The following object is masked from 'package:base':
##
##     gamma

stock_tick <- sstock()

### sstock()

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)

delta()

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

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)

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