8.15 The gamma and vega of a delta-neutral portfolio are 50 and 25, respectively, where

the vega is "per %." Estimate what happens to the value of the portfolio when there is a shock to the market causing the underlying asset price to decrease by $3 and

its volatility to increase by 4%.

8.17 A financial institution has the following portfolio of over-the-counter options on

pounds sterling:

Delta of Gamma of Vega of

Type Position Option Option Option

Call 1,000 0.50 2.2 1.8

Call 500 0.80 0.6 0.2

Put 2,000 0.40 1.3 0.7

Call 500 0.70 1.8 1.4

A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

(a) What position in the traded option and in pounds sterling would make the

portfolio both gamma neutral and delta neutral?

(b) What position in the traded option and in pounds sterling would make the

portfolio both vega neutral and delta neutral?