35.

You are given the following information on shares and European-style call and put options on BFC Ltd. BFC shares are currently trading at $20.00. Each option is over one share. Use the numbers exactly as given in the table below to do your calculations.

Black Scholes Merton option price calculation
stock price	20.00	20.00
strike price	20.00	21.00
interest rate	0.040	0.040
volatility	0.200	0.200
time to maturity (years)	0.500	0.500
d1	0.212	-0.133
N(d1)	0.584	0.447
d2	0.071	-0.274
N(d2)	0.528	0.392
BSM call option	1.3254	0.8754
N(-d1)	0.4160	0.5529
N(-d2)	0.4718	0.6081
BSM put option	0.9294	1.4596
delta(Call)	0.5840	0.4471
delta(Put)	-0.4160	-0.5529
gamma	0.1379	0.1398
vega(answer in cents)	5.5164	5.5923
theta call	-1.5175	-1.4412
theta put	-0.7333	-0.6178
rho(call)(answer in cents)	5.1773	4.0338
rho(put)(answer in cents)	-4.6247	-6.2583

Answer the following questions.

1. You construct a portfolio consisting of 1500 long call options at an exercise price of $21.00 and 1000 short put options at an exercise price of $20.00 over BFC shares. The cost to set the portfolio up is $---------. Give your answer correct to 2 decimal places or your answer will be incorrect.

2. The delta of your portfolio of options (constructed in part 1) is --------. Give your answer correct to 2 decimal places or your answer will be incorrect.

Ignore the portfolio you have created in parts 1. and 2. of this question.

3. You now want to construct a gamma neutral portfolio using only the 1500 long call options (strike = $21) and a position in the put options (Strike = $20). In order to achieve this you must establish a -------(short/long) position in ---------put options to make your portfolio gamma neutral. (Here write the number of put options to the nearest whole number).

4. But your aim is to achieve a delta neutral and gamma neutral portfolio. You therefore want to make the portfolio constructed in part 3 delta neutral by adding the appropriate position in shares to your portfolio. You must add a ------(long/short) position in ------ shares to the portfolio of options. (Here write the number of shares rounded to the nearest whole number).

Do NOT include the dollar sign ($) in any answer.