Sunny Bank has the following portfolio of over-the-counter options on the same underlying asset:

Type

Position

Delta of Option

Gamma of Option

Vega of Option

Call

-1,000

0.2

0.9

1.6

Call

600

0.8

0.5

1.0

Put

-2,000

-0.4

1.4

0.5

(a)Calculate the delta, gamma and vega of the portfolio.

(b)One traded option is available. It has a delta of 0.8, a gamma of 4.0, and a vega of 2.0. How can the bank make the portfolio both delta and vega neutral?

(c)Two traded options are available. The first has a delta of 0.8, a gamma of 4.0, and a vega of 2.0. The second traded option has a delta of 0.5, a gamma of 2.0, and a vega of 5.0. How can the bank make the portfolio delta, gamma, and vega neutral?

(d)What is meant by the gamma of an option? How can you interpret a call option gamma of 0.9? What are the risks in the situation where the gamma of a position is large and negative and the delta is zero?