Reference no: EM133059974
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 calculations. Data in the first column pertains to $20 strike options. Data in the second column pertains to $21 strike options.
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Black Scholes Merton option price calculation
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stock price
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20.00
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20.00
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strike price
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20.00
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21.00
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interest rate
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0.040
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0.040
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volatility
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0.200
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0.200
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time to maturity (years)
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0.500
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0.500
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d1
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0.212
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-0.133
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N(d1)
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0.584
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0.447
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d2
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0.071
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-0.274
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N(d2)
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0.528
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0.392
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BSM call option
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1.3254
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0.8754
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N(-d1)
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0.4160
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0.5529
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N(-d2)
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0.4718
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0.6081
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BSM put option
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0.9294
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1.4596
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delta(Call)
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0.5840
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0.4471
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delta(Put)
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-0.4160
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-0.5529
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gamma
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0.1379
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0.1398
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vega(answer in cents)
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5.5164
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5.5923
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theta call
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-1.5175
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-1.4412
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theta put
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-0.7333
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-0.6178
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rho(call)(answer in cents)
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5.1773
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4.0338
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rho(put)(answer in cents)
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-4.6247
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-6.2583
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Answer the following questions.
1. You construct a portfolio consisting of 1700 long call options at an exercise price of $21.00 and 1500 short put options at an exercise price of $20.00 over BFC shares. The cost to set the portfolio up is $Answer. 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 Answer. 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 1700 long call options (strike = $21) and a position in the put options (Strike = $20). In order to achieve this you must establish a Answer shortlong position in Answer put options to make your portfolio gamma neutral. (Here write the number of put options to the nearest whole number).
4. But your aim is to achieve a delta neutral and gamma neutral portfolio. You therefore want to make the portfolio constructed in part 3 delta neutral by adding the appropriate position in shares to your portfolio. You must add a Answershortlong position in Answer shares to the portfolio of options. (Here write the number of shares rounded to the nearest whole number).
Do NOT include the dollar sign ($) in any answer. Do NOT include a comma in any answer.