## [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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