#
# Example:
#	Investigate the Smile Effect
#
# Description:
#	This program calculates for the estimated symmetric and asymmetric
#	Garch(1,1) the implied volatility from the Black and Scholes Option
#	Pricing formula assuming that the real market follows ideally the
#	Heston Nandi Option Garch(1,1) model
#
# Author:
#	(C) 2002, Diethelm Wuertz, GPL
#


# ------------------------------------------------------------------------------
 	
 	
# Show the GBSVolatility function:

    GBSVolatility

# Compute Smile:

	# Parameters:
	S  = 85:115; X = 100
	Time.inDays = 126 
	model = list(lambda=-0.5, omega=6e-6, alpha=4e-6, beta=0.8, gamma=0)
	sigma = sqrt(252*(model$alpha+model$omega)/(1-model$beta))
	sigma
	
	# Put:
	Put <- impVola <- NULL
	for (i in 1:length(S)) {
		Price = HNGOption("p", model, S[i], X, Time.inDays, 0)$price
		Put = c(Put, Price) 
		Volatility = GBSVolatility(Price, "p", S[i], X, Time.inDays/252, 0, 0)
		impVola = c(impVola, Volatility)
		cat("\n\t", i, "\t", S[i], "\t", Price, "\t", Volatility) }
		
# Plot:

	par(mfrow = c(2, 2), cex = 0.7)
	plot(S/X, Put, 
		xlab = "S/X", ylab = "Price", main = "HN Put Price")
	plot(S/X, impVola, 
		xlab = "S/X", ylab = "Volatility", main = "BS Implied Volatility")