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

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)

Example output

Loading required package: mvtnorm
Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries
Quanto American Put Option
Price: 0.1240409Quanto American Put Option
Price: 2.446458
Quanto American Put Option
Method: Simple Least Squares Monte Carlo
                                   
Option price               2.446458
Spot price                 14.2    
Strike                     16.5    
Volatility                 0.2     
Number of paths            200     
Number of time-steps       50      
Interest rate              0.06    
Dividend rate              0       
Maturity time              1       
Spot price of 3rd asset    1       
Volatility of 3rd asset    0.2     
Interest rate of 3rd asset 0       
Dividend rate of 3rd asset 0       
Correlation coefficient    0       
[1] 2.446458

LSMonteCarlo documentation built on May 2, 2019, 8:55 a.m.