BlackScholesCallESSim function

ES of Black-Scholes call using Monte Carlo Simulation

Estimates ES of Black-Scholes call Option using Monte Carlo simulation

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

Arguments

• amountInvested: Total amount paid for the Call 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
• cl: Confidence level for which ES is computed and is scalar
• hp: Holding period of the option in days and is scalar

Returns

ES

Examples

# Market Risk of American call with given parameters.
   BlackScholesCallESSim(0.20, 27.2, 25, .16, .2, .05, 60, 30, .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.