Block Scholes for Geometric Asian Call Option

Description

Function to calculate expected value of Geometric Asian Call Option via Block Scholes formula.

Usage

BS_Asian_geom(K = 100, TimeToMat, d, ti, r = 0.05, sigma = 0.1, S0 = 100, ...)

Arguments

Value

Expected value of Geometric Average Asian Call Option, vector of control points, interest rate and strike price as a list.

Examples

 sim.outer(n=1e3, d=3, q.outer = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

Block Scholes for Geometric Asian Call Option

Description

Function to calculate expected value of Geometric Asian Call Option via Block Scholes formula.

Usage

myq_asian(zm, K = 100, ti = (1:3)/12, r = 0.05, sigma = 0.1, S0 = 100)

Arguments

Value

Returns 4 elements as a list. Asian Call Option Prices, Last Price of Asian Call Option, Expected Value of Asian Call Option, Product of the prices through time

Examples

 sim.outer(n=1e3, d=3, q.outer = sim.IS,
q.is = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

Euclidean Distance

Description

Function to calculate euclidean distance between two vectors.

Usage

myq_euclidean(zm, point = c(1, 2, 1))

Arguments

Value

Sum of the euclidean distance from point to set of vectors.

Examples

sim.outer(n=1e3, d=3, q.outer=myq_euclidean, point=c(1,1,1))

Function to apply Antithetic Variates Algorithm.

Description

Given matrix input with d dimension, this function runs simulation two times using positive and negative signed versions of the input matrix.

Usage

sim.AV(zm, q.av, ...)

Arguments

Value

y target vector with theoretically lower variance with the same expected value as the initial y vector.

Examples

 sim.outer(n=1e3, d=3, q.outer = sim.AV,
q.av = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

sim.outer(n=1e3, d=3, q.outer = sim.AV, q.av = sim.InnerCV,
q.cv = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

An Outer Control Variate function for Asian Call Option.

Description

# Applies geometric average asian call outer control varites algorithm to the simulation. Gets expected value for the control variate using BS_Asian_geom function if IS algorithm is within the framework, the length of the q.ga will be different. Checks if IS algorithm is within the framework and applies IS weight accordingly.

Usage

sim.GeometricAvg(zm, q.ga, ...)

Arguments

Value

Updates Y value which stored in list 'results' and returns the list 'results' with updated Y value.

Examples

 sim.outer(n=1e3, d=3, q.outer = sim.GeometricAvg,
q.ga = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

sim.outer(n=1e3, d=1, q.outer = sim.AV, q.av = sim.GeometricAvg,
q.ga = myq_asian, K=90, ti=(1:1/12), r=0.03, sigma=0.3, S0=100)

Function to apply Importance Sampling Algorithm.

Description

Given matrix input with d dimension, this function applies Importance Sampling algorithm and it chooses the best value of the mean value of the importance density automatically. Performs better in rare event simulation. sim.IS checks the input size and returns elements accordingly. If the input value is a list of one element it only updates the simulated value with importance weight and returns that value. If the input value has a dimension bigger than 1, weight values are added separately as another input of the list.

Usage

sim.IS(zm, use_pilot_study = TRUE, muis = 1, sis = 1, q.is, ...)

Arguments

Value

Weighted simulated values or weights and simulated values are added to input list depending on the initial input size.

Examples

 sim.outer(n=1e3, d=3, q.outer = sim.IS,
q.is = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

sim.outer(n=1e5, d=4, q.outer=sim.AV, q.av = sim.IS, q.is = myq_asian,
         K=130, ti=(1:4/12), r=0.03, sigma=0.3, S0=100)

Function to apply Inner Control Variates Algorithm.

Description

Given matrix input with d dimension, this function aims to reduce the variance by applying Inner Control Variates algorithm. It uses input columns and their squares as inner control variates and applies feature selection for these control variates.

Usage

sim.InnerCV(zm, q.cv, ...)

Arguments

Value

Updates Y value which stored in list 'results' and returns the list 'results' with updated Y value.

Examples

 sim.outer(n=1e3, d=3, q.outer = sim.InnerCV,
q.cv = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)

sim.outer(n=1e6, d=6, q.outer = sim.AV, q.av = sim.InnerCV,
q.cv = myq_asian, K=105, ti=(1:6/12), r=0.03, sigma=0.3, S0=100)

Main function for VarRedOpt simulation framework.

Description

This function creates the z matrix which is an input matrix with given dimension value, d, and given length, n. Values are generated from standard normal distribution. After creating the z matrix, this function sends this input matrix to given simulation function. After simulation steps are completed, simulate.outer function gets the final simulated values and calculates expected value and variance. For instance, if myq_asian and sim.AV functions are given in simulate.outer function as parameters, the input matrix will be sent to sim.AV function and sim.AV function will send input value to myq_asian function twice with opposite signs and gets simulation results. After collecting these results it applies Antithetic Variates algorithm and finds the final simulation value and sends it back to the simulate.outer function.

Usage

sim.outer(n, d, auto_repetition = 1, q.outer, ...)

Arguments

Value

estimation mean, standard error, confidence interval metrics if auto_repetition = TRUE

Examples

 sim.outer(n=1e3, d=3, q.outer = sim.AV,
q.av = myq_asian, K=100, ti=(1:3/12), r=0.03, sigma=0.3, S0=100)