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.

Package: | OptionPricing |

Type: | Package |

Version: | 0.1 |

Date: | 2014-11-07 |

License: | License: GPL-2 | GPL-3 |

Copyright: | Wolfgang Hormann |

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.

Kemal Dingec, Wolfgang Hormann

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
# 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)
``` |

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