HestonNandiOptions: Option Price for the Heston-Nandi Garch Option Model

In fOptions: Rmetrics - Pricing and Evaluating Basic Options

Description

A collection and description of functions to valuate Heston-Nandi options. Included are functions to compute the option price and the delta and gamma sensitivities for call and put options.

The functions are:

HNGOption	Heston-Nandi GARCH(1,1) option price,
HNGGreeks	Heston-Nandi GARCH(1,1) option sensitivities,
HNGCharacteristics	option prices and sensitivities.

Usage

HNGOption(TypeFlag, model, S, X, Time.inDays, r.daily)
HNGGreeks(Selection, TypeFlag, model, S, X, Time.inDays, r.daily)
HNGCharacteristics(TypeFlag, model, S, X, Time.inDays, r.daily)

Arguments

model	a list of model parameters with the following entries: lambda, omega, alpha, beta, and gamma, numeric values.
r.daily	the daily rate of interest, a numeric value; e.g. 0.25/252 means about 0.001% per day.
S	the asset price, a numeric value.
Selection	sensitivity to be computed, one of "delta", "gamma", "vega", "theta", "rho", or "CoC", a string value.
Time.inDays	the time to maturity measured in days, a numerical value; e.g. 5/252 means 1 business week.
TypeFlag	a character string either "c" for a call option or a "p" for a put option.
X	the exercise price, a numeric value.

Details

Option Values:

HNGOptioncalculates the option price, HNGGreeks allows to compute the option sensitivity Delta or Gamma, and HNGcharacterisitics summarizes both in one function call.

Value

HNGOption
returns a list object of class "option" with $price denoting the option price, a numeric value, and $call a character string which matches the function call.

HNGOGreeks
returns the option sensitivity for the selected Greek, either "delta" or "gamma"; a numeric value.

HNGCharacteristics
returns a list with the following entries:

premium	the option price, a numeric value.
delta	the delta sensitivity, a numeric value.
gamma	the gamma sensitivity, a numeric value.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

References

Heston S.L., Nandi S. (1997); A Closed-Form GARCH Option Pricing Model, Federal Reserve Bank of Atlanta.

Examples

## model -
   # Define the Model Parameters for a Heston-Nandi Option:
   model = list(lambda = -0.5, omega = 2.3e-6, alpha = 2.9e-6, 
     beta = 0.85, gamma = 184.25) 
   S = X = 100
   Time.inDays = 252
   r.daily = 0.05/Time.inDays
   sigma.daily = sqrt((model$omega + model$alpha) /
     (1 - model$beta - model$alpha * model$gamma^2))
   data.frame(S, X, r.daily, sigma.daily)

## HNGOption -
   # Compute HNG Call-Put and compare with GBS Call-Put:
   HNG = GBS = Diff = NULL
   for (TypeFlag in c("c", "p")) {
     HNG = c(HNG, HNGOption(TypeFlag, model = model, S = S, X = X, 
       Time.inDays = Time.inDays, r.daily = r.daily)$price )
     GBS = c(GBS, GBSOption(TypeFlag, S = S, X = X, Time = Time.inDays, 
       r = r.daily, b = r.daily, sigma = sigma.daily)@price) }
   Options = cbind(HNG, GBS, Diff = round(100*(HNG-GBS)/GBS, digits=2))
   row.names(Options) <- c("Call", "Put")
   data.frame(Options)
     
## HNGGreeks -
   # Compute HNG Greeks and compare with GBS Greeks:
   Selection = c("Delta", "Gamma")
   HNG = GBS = NULL
   for (i in 1:2){
     HNG = c(HNG, HNGGreeks(Selection[i], TypeFlag = "c", model = model, 
       S = 100, X = 100, Time = Time.inDays, r = r.daily) ) 
     GBS = c(GBS, GBSGreeks(Selection[i], TypeFlag = "c", S = 100, X = 100, 
       Time = Time.inDays, r = r.daily, b = r.daily, sigma = sigma.daily) ) }
   Greeks = cbind(HNG, GBS, Diff = round(100*(HNG-GBS)/GBS, digits = 2))
   row.names(Greeks) <- Selection
   data.frame(Greeks)

Example output

Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics


Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: [e-mail]


Rmetrics Package fOptions
Pricing and Evaluating Basic Options
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: [e-mail]
    S   X      r.daily sigma.daily
1 100 100 0.0001984127  0.01004349
          HNG      GBS Diff
Call 8.992100 8.939049 0.59
Put  4.115042 4.061991 1.31
             HNG        GBS  Diff
Delta 0.67395339 0.65295993  3.22
Gamma 0.02211149 0.02315963 -4.53

fOptions documentation built on May 2, 2019, 2:27 p.m.