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[answered] Assume MBS model for risky asset S, pays no dividends, S0 =

Assume MBS model for risky asset S, pays no dividends, S0 = 60, volatility 30% and risk free rate 8%. We also have the following information on two call options on S and Black-Scholes value on price and Greeks.

Call option | A | B |

Time | 90 days | 60 days |

Strike price | 60 | 65 |

Option value | 4.14452 | 1.37826 |

Delta | 0.581957 | 0.312373 |

Gamma | 0.043688 | 0.048502 |

Assume that there are 365 days in one year (so that time on A is for example T = 90/365). We sell 1000 derivatives of A and we want to hedge portfolios against risk, which we finance with bank account (that is, starting value of the portfolio is 0 with regards to value in the bank account, which can be both positive and negative).

- a) Set up a portfolio in the beginning that is delta-neutral, use only S to hedge.

b) Set up a portfolio in the beginning that is delta- and gamma neutral. Only use S and B to hedge.

c) Show in a table the value of the portfolios (a) and (b) after one day (delta t = ), assume the price of underlying stock is between 58-62, with step 0.5

d) Show in a table the value of the portfolios (a) and (b) after one day (delta t = ), assume the price of underlying stock is between 50-70, with step 5?

Assume MBS model for risky asset S, pays no dividends, S0 = 60, volatility

30% and risk free rate 8%. We also have the following information on two

call options on S and Black-Scholes value on price and Greeks.

Call option

Time

Strike price

Option

value

Delta

Gamma A

90 days

60

4.14452 B

60 days

65

1.37826 0.581957

0.043688 0.312373

0.048502 Assume that there are 365 days in one year (so that time on A is for

example T = 90=365). We sell 1000 derivatives of A and we want to

hedge portfolios, which we finance with bank account (that is, starting

value of the portfolio is 0 with regards to value in the bank account, which

can be both positive and negative).

a) Set up a portfolio in the beginning that is delta-neutral, use only S to

hedge.

b) Set up a portfolio in the beginning that is delta- and gamma neutral.

Only use S and B to hedge.

c) Show in a table the value of the portfolios (a) and (b) after one day

(delta t = 1=365), assume the price of underlying stock is between

58-62, with step 0.50

d) Show in a table the value of the portfolios (a) and (b) after one day (delta t = 1=365), assume the price of underlying stock is between

50-70, with step 5

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