AmericanPutESSim function

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

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.

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

Returns

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

Examples

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

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.