# QuantoAmerPutLSM: Calculating the price of Quanto American put In LSMonteCarlo: American options pricing with Least Squares Monte Carlo method

## Description

The function calculates the price of Quanto American put with Least Squares Monte Carlo method. The Quanto option is cash-settled option, whose pay-off is converted into a third currency/asset at exercise at a pre-specified rate/price (Wystup, 2011), and can also be considered as a usual option but settled in a "wrong" asset (Vecer, 2011). The regression model included in the algorithm is quadratic polynomial (Longstaff & Schwartz, 2000).

## Usage

 ```1 2 3 4 5 6 7``` ```QuantoAmerPutLSM(Spot = 1, sigma = 0.2, n = 1000, m = 365, Strike = 1.1, r = 0.06, dr = 0, mT = 1, Spot2 = 1, sigma2 = 0.2, r2 = 0, dr2 = 0, rho = 0) ## S3 method for class 'QuantoAmerPut' print(x, ...) ## S3 method for class 'QuantoAmerPut' 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. USD). `dr` Dividend rate of the underlying asset. `mT` Maturity time (years). `Spot2` Spot price of the 3rd asset (e.g. EUR/USD). `sigma2` Volatility of the 3rd asset. `r2` Interest rate of the 3rd asset. `dr2` Dividend rate of the 3rd asset. `rho` Correlation coefficient between the prices. `x` An object returned by the functions `QuantoAmerPutLSM`. `object` An object returned by the function `QuantoAmerPutLSM`. `...` Not used.

## Value

The function returns an object of the class QuantoAmerPut 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.

## Note

The function `rmvnorm` included in the pricing algorithm is a part of the mnormt package. Please, load that package before the use of the `QuantoAmerPutLSM` 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.

Vecer, J. 2011. Stochastic Finance: A Numeraire Approach. CRC Press.

Wystup, U. 2011. Quanto Options. MathFinance AG.

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