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

1

1.8

Call

500

0.8

0.6

1.2

Put

-2,000

-0.4

1.5

0.6

(a)Calculate the delta, gamma and vega of the portfolio. [6 marks]

(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 gamma neutral? [5 marks]

(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 3.0, and a vega of 2.0. How can the bank make the portfolio delta, gamma, and vega neutral? [8 marks]

(d)What is meant by the vega of an option? How can you interpret a call option vega of 1.8? What are the risks in the situation where the vega of a position is large and negative? [4 marks]