Estimates ES of American vanilla put using binomial option valuation tree and Monte Carlo Simulation

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Description

Estimates ES of American Put Option using binomial tree to price the option valuation tree and Monte Carlo simulation with a binomial option valuation tree nested within the MCS. Historical method to compute the VaR.

Usage

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AmericanPutESSim(amountInvested, stockPrice, strike, r, mu, sigma, maturity,
  numberTrials, numberSteps, cl, hp)

Arguments

amountInvested

Total amount paid for the Put Option and is positive (negative) if the option position is long (short)

stockPrice

Stock price of underlying stock

strike

Strike price of the option

r

Risk-free rate

mu

Expected rate of return on the underlying asset and is in annualised term

sigma

Volatility of the underlying stock and is in annualised term

maturity

The term to maturity of the option in days

numberTrials

The number of interations in the Monte Carlo simulation exercise

numberSteps

The number of steps over the holding period at each of which early exercise is checked and is at least 2

cl

Confidence level for which VaR is computed and is scalar

hp

Holding period of the option in days and is scalar

Value

Monte Carlo Simulation VaR estimate and the bounds of the 95 confidence interval for the VaR, based on an order-statistics analysis of the P/L distribution

Author(s)

Dinesh Acharya

References

Dowd, Kevin. Measuring Market Risk, Wiley, 2007.

Lyuu, Yuh-Dauh. Financial Engineering & Computation: Principles, Mathematics, Algorithms, Cambridge University Press, 2002.

Examples

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# Market Risk of American Put with given parameters.
   AmericanPutESSim(0.20, 27.2, 25, .16, .2, .05, 60, 30, 20, .95, 30)

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