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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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