# 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.