portfolio_valuation: Calculate payoffs from trajectories

In mociepa/ShortfallRiskHedging: Shortfall Risk Hedging for european option

Calculate payoffs from trajectories

Description

The portfolio_valuation function determines the value of the portfolio while option hedging.

Usage

portfolio_valuation(option_value, rate, Xi, asset_price, End_Time = 1, initial_capital = 0)

Arguments

option_value	numeric value, option price at the beginning of the simulations.
rate	numeric value, risk free rate in the model, rate >= 0.
Xi	numeric vector, number of asset needed to hedge an option over time.
asset_price	numeric vector, price oft the asset over time.
End_Time	numeric value, end time of the option.
initial_capital	numeric value, the amount of money we want to add to the portfolio at time 0.

Details

In theory hedging give us full protection against the option. Due to discretization of the Black-Scholes model in simulations we can have some losses or gains during time. portfolio_valuation function calculate this gains/losses over time.

initial_capital is the initial amount, if we were to use the incomplete initial price of the option to insure against it. For example: Price of the european call option is 5, to hedge this option we will hedge some modification of this option with the inital price 4. Now we can set initial_capital = 1, which we add at the beginning of the hedging, and grow according with the risk free rate.

Value

A numeric vector, value of the hedging portfolio over time.

Examples

x <- generate_scenarios(100, 0.05, 0.3) #real measure
time_period <- seq(0, 1, 1/250)
option <- call_price(x[, 1], 100, 0, 0.3, time_period, 1)
Xi <- Xi_call_price(x[, 1], 100, 0, 0.3, time_period, 1)
portfolio_valuation(option[1], 0, Xi, x[, 1])

mociepa/ShortfallRiskHedging documentation built on Sept. 30, 2022, 6:43 p.m.