LSMonteCarlo (version 1.0)

AmerPutLSM_CV: Pricing plain vanilla American put with Control Variates

Description

The function calculates the price of a plain vanilla American put with Least Squares Monte Carlo method with Control Variates (Glasserman, 2004). Black & Scholes solution for European put is used as the control. The regression model included in the algorithm is quadratic polynomial (Longstaff & Schwartz, 2000).

Usage

AmerPutLSM_CV(Spot = 1, sigma = 0.2, n = 1000, m = 365, Strike = 1.1, r = 0.06, 
dr = 0, mT = 1)
"print"(x, ...)
"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_CV.

object

An object returned by the function AmerPutLSM_CV.

...

Not used.

Value

The function returns an object of the class AmerPutCV 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.

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.

See Also

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

Examples

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