What difference does it make to the worst-case scenario in Example 19.1 if (a) the options are American rather than European and (b) the options are barrier options that are knocked out if the asset price reaches $65? Use the DerivaGem Applications Builder in conjunction with Solver to search over asset prices between $40 and $60 and volatilities between 18% and 30%.

EXAMPLE 19.1

As a simple example of reverse stress testing, suppose a financial institution has positions in four European call options on an asset. The asset price is $50, the risk-free rate is 3%, the volatility is 20%, and there is no income on the asset. The positions, strike prices, and times to maturity are as indicated in the table below. The current value of the position (in $000s) is %u221225.90. The DerivaGem Application Builder can be used to search for one-day changes in the asset price and the volatility that will lead to the greatest losses. Some bounds should be put on the changes that are considered. We assume that the asset price will not decrease below $40 or increase above $60. It is assumed that the volatility will not fall below 10% or rise above 30%.