# OptionPricing-package: Option Pricing and Greeks Estimation for Asian and European... In OptionPricing: Option Pricing with Efficient Simulation Algorithms

## 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.

## 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.

## Author(s)

Kemal Dingec, Wolfgang Hormann

## Examples

 ``` 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) ```

### Example output

```          result error estimate
price 6.15604078   2.919861e-08
delta 0.59385393   3.985961e-09
gamma 0.03057798   5.816272e-10
[1] 6.15604
result error estimate
price 1.522917e-04   3.947613e-09
delta 5.091268e-05   9.319224e-10
gamma 1.578448e-05   1.864355e-10
[1] 0.0001524371
[1] 6.15604
price      delta      gamma
4.61499713 0.56946018 0.05694602
price       delta       gamma
3.37277718 -0.43053982  0.05694602
```

OptionPricing documentation built on May 29, 2017, 8:29 p.m.