QuantoAmerPutLSM {LSMonteCarlo}

Calculating the price of Quanto American put

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

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.

See Also

Functions: price, QuantoAmerPutLSM_AV, AmerPutLSM, AsianAmerPutLSM, and AmerPutLSM_AV.

Examples

QuantoAmerPutLSM(n=200, m=50)
put<-QuantoAmerPutLSM(Spot=14.2, Strike=16.5, n=200, m=50)
put
summary(put)
price(put)