Question

A stock option market maker has a portfolio consisting of 200 shares
of ABC Corp, and the following option positions on ABC Corp. For simplicity, each
option is assumed to be written on a single share of the stock.

Quantity	Exercise Price	Option Type	Price	Delta	Gamma
100		Stock	120	1	0
150	120	Call	4,3585	0,5362	0,0385
-120	125	Call	4,1383	0,4179	0,0268
100	115	Put	4,1947	-0,3289	0,0202
-100	130	Call	3,5891	0,2982	0,0238

The market maker is worried about stock price movements in ABC's stock and would
like to make his portfolio delta-neutral and gamma neutral over the night. The current
stock price of ABC is $120, the volatility of the stock is 30%, and the risk-free rate is
5%. The market maker can form the hedge using a futures on ABC stock whose price
is at full carry and either one of two options on ABC stock whose attributes are

Exercise Price	Option Type	Price	Delta	Gamma
110	Put	1,7220	-0,1994	0,0191
125	Call	2,3255	0,3505	0,0359

(a) (10 points) How many futures and option contracts should be bought or sold if
he uses futures and call option?
(b) (10 points) How many futures and option contracts should be bought or sold if
he uses futures and put option?
(c) (10 points) If transaction costs are $ 5 per contracts, which instruments should
be selected to achieve delta-neutral and gamma-neutral?

Answer 1

excercise price	pot type	price	delta	gamma
110	p	1.7220	-0.1994	0.0191
125	c	2.3255	0.3505	0.0359

The current price stock price is $120

Volatility of the stock is 30%

And the risk free rate is 5%

a) Sell 10 put options—each options contract is for 110 shares—with a strike price.

b) .the buyer of the call option for 125 shares the right to buy a stock from you at a certain price by a certain date