AmerPutLSM_AV: Pricing plain vanilla American put with Antithetic Variates In LSMonteCarlo: American options pricing with Least Squares Monte Carlo method

Description

The function calculates the price of a plain vanilla American put with Least Squares Monte Carlo method with Antithetic Variates (Glasserman, 2004). The regression model included in the algorithm is quadratic polynomial (Longstaff & Schwartz, 2000).

Usage

 ```1 2 3 4 5 6 7``` ```AmerPutLSM_AV(Spot = 1, sigma = 0.2, n = 1000, m = 365, Strike = 1.1, r = 0.06, dr = 0, mT = 1) ## S3 method for class 'AmerPutAV' print(x, ...) ## S3 method for class 'AmerPutAV' summary(object, ...) ```

Arguments

 `Spot` Spot price of the underlying asset (e.g. stock). `sigma` Volatility of the underlying asset. `n` Number of paths simulated. `m` Number of time steps in the simulation. `Strike` Strike price of the option. `r` Interest rate of the numeraire currency (e.g. EUR). `dr` Dividend rate of the underlying asset. `mT` Maturity time (years). `x` An object returned by the functions `AmerPutLSM_AV`. `object` An object returned by the function `AmerPutLSM_AV`. `...` Not used.

Value

The function returns an object of the class AmerPutAV that is a list comprising the price calculated and the entry parameters. Class-specific `print` function gives the option type information and the price. The price as a single number can be derived using the `price` function. An overview of the entire object can be seen using the `summary` function.

Author(s)

Mikhail A. Beketov

References

Glasserman, P. 2004. Monte Carlo Methods in Financial Engineering. Springer.

Longstaff, F.A., and E.S. Schwartz. 2000. Valuing american option by simulation: A simple least-squared approach. The Review of Financial Studies. 14:113-147.

Functions: `price`, `AmerPutLSM`, `AmerPutLSM_CV`, `AsianAmerPutLSM`, and `QuantoAmerPutLSM`.
 ```1 2 3 4 5 6``` ```AmerPutLSM_AV(n=500, m=50) put<-AmerPutLSM_AV(Spot=14.2, Strike=16.5, n=200, m=50) put summary(put) price(put) put\$price ```