# AmerPutLSM: Calculating the price of plain vanilla American put In LSMonteCarlo: American options pricing with Least Squares Monte Carlo method

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```AmerPutLSM(Spot = 1, sigma = 0.2, n = 1000, m = 365, Strike = 1.1, r = 0.06, dr = 0, mT = 1) ## S3 method for class 'AmerPut' print(x, ...) ## S3 method for class 'AmerPut' 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`. `object` An object returned by the function `AmerPutLSM`. `...` Not used.

## Value

The function returns an object of the class AmerPut that is a list comprising the price calculated, option type, 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

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_AV`, `AmerPutLSM_CV`, `AsianAmerPutLSM`, and `QuantoAmerPutLSM`.

## Examples

 ```1 2 3 4 5 6``` ```AmerPutLSM() put<-AmerPutLSM(Spot=14.2, Strike=16.5, n=500, m=100) put summary(put) price(put) put\$price ```

### Example output

```Loading required package: mvtnorm

Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
American Put Option
Price: 0.1173262American Put Option
Price: 2.307947
American Put Option
Method: Simple Least Squares Monte Carlo

Option price         2.307947
Spot price           14.2
Strike               16.5
Volatility           0.2
Number of paths      500
Number of time-steps 100
Interest rate        0.06
Dividend rate        0
Maturity time        1
[1] 2.307947
[1] 2.307947
```

LSMonteCarlo documentation built on May 29, 2017, 11:08 p.m.