OptionPricing (version 0.1.2)

OptionPricing-package: Option Pricing and Greeks Estimation for Asian and European Options

Description

The Price, Delta and Gamma of European and Asian Options under Geometric Brownian Motion are calculated using the Black-Scholes formula and Efficient Monte Carlo and Randomized Quasi Monte Carlo Algorithms.

Author

Kemal Dingec, Wolfgang Hormann

Details

The OptionPricing package calculates the Price, Delta and Gamma for European options using the Black-Scholes formula (see BS_EC). The price, Delta and Gamma for Asian call options under geometric Brownian motion are calculated using a very efficient Monte Carlo and randomized quasi-Monte Carlo algorithm (see AsianCall). The function AsianCall_AppLord implements a high-quality approximation for the price of an Asian option.

Examples

# standard settings for an efficient simulation using QMC and variance reduction
AsianCall(T=1,d=12,K=100,r=0.05,sigma=0.2,S0=100,method=c("best"),
  sampling=c("QMC"),metpar=list(maxiter=100,tol=1.e-14,cvmethod="splitting"),
  sampar=list(nout=50,n=2039,a=1487,baker=TRUE,genmethod="pca"))

# Calculation of the Price of an Asian option using a good approximation  
  AsianCall_AppLord(T = 1, d = 12, K = 100, r = 0.05, sigma = 0.2, S0 = 100)


# standard settings for an efficient simulation using MC and variance reduction
AsianCall(T=1,d=12,K=170,r=0.05,sigma=0.2,S0=100,method="best",
          sampling="MC",metpar=list(maxiter=100,tol=1.e-14,np=1000),
		  sampar=list(n=10^5))
# Calculation of the approximate price, a bit different to the above result 
  AsianCall_AppLord(T = 1, d = 12, K = 170, r = 0.05, sigma = 0.2, S0 = 100)
  
# Calculation of the Price of an Asian option using a good approximation  
  AsianCall_AppLord(T = 1, d = 12, K = 100, r = 0.05, sigma = 0.2, S0 = 100)

#Price, Delta and Gamma of European options using Black-Scholes  
BS_EC(K=100, r = 0.05, sigma = 0.2, T = 0.25, S0 = 100)
BS_EP(K=100, r = 0.05, sigma = 0.2, T = 0.25, S0 = 100)