1. Suppose two-period (years) ATM European up and in call options, whose underlying stock has current price of $100 with a degree of up movement of 30% and down movement of 10% for each year. The risk-free annual rate is 10%. The knock in barrier B = $110 and Rebate = B-K. (1) Please find the premium of call. (2) if the knock in barrier B = $140, find the premium. (3) how do you feel that relationship between barriers and premiums for up and in call.

2. Suppose three-period (years) ATM Bermudan put options, whose underlying stock has current price of $100 with a degree of up movement of 30% and down movement of 10% for each year. The risk-free annual rate is 10%. Please find the premium of Bermudan put, if the holder of put has right to early exercise his right just at second period.

3. Suppose two-period (years) bonus enhanced note with two strike prices of K1=$100, and K2= $140, whose underlying stock price of $100 with a degree of up movement of 30% and down movement of 10% for each year. The risk-free annual rate is 10% and the constant bonus is $40. Please find the fair price of bonus enhanced note.

4. E-Sun Options: an option if all stocks from the underlying basket of securities hit and over a predetermined barrier. A one-period E-Sun call option on three assets S (F) [V] whose current price $100 ($110) [$106] with a constant growth rate of 10% (8%) [12%] and a declining rate of 10% (8%) [6%] in price. The risk-free rate of one period is 5% and the strike price is $100. The barrier is B = $111. The relationship of movements in asset prices is assumed to be independent. The holder can exercise the options or abandon his right. Please find the premium of E-Sun option at time 0.

5. There are three regular coupon bonds (I, II, III), please converse them into zero-coupon bonds (A, B, C, D) and value the current prices for these zero-coupon bonds if market interest rate is 5% constantly. Regular coupon bond I: $200 par value, 4 years, 8% coupon rate; Regular coupon bond II: $500 par value, 2 years, 10% coupon rate; Regular coupon bond III: $400 par value, 3 years, 8% coupon rate.

6. Please pricing default-able bonds with 2 years, face value (F) of $1,000,000, firm value (V) of 1,200,000. The firm values volatility rate is 10% and risk-free rate is 5%. (1) the value of default-able bond; (2) the quasi debt-to-value ratio; (3) the probability of defaulting for the firm of debt issuing.

7. Please design a bear-viewpoint ELN with face value (FV) of zero-coupon bond, and a shorting position of call option on the index (S) with a strike price K. (1) Showing a mathematical equation for the ELN at maturity. (2) How many units of call options should be sold. (3) Plotting the diagram of the net payoffs for the ELN.

8. Plot following PGN contracts terminal payoffs

Issuer: JP Morgan

Linked underlyings: ABC shares

Maturity: 2 years

Investment price: principal

Entering price for trading: closing price at starting date

Strike: 75%* entering price

Coupon: 9%

Payoffs:

First year, get 7% coupon

Second year,

If the performance stocks return rate is over -10%

If the performance stocks return rate is less than -10%

9. A three-period (years) model for pricing senior bond, junior bond, and equity, whose underlying firms initial asset value (V) of $1,000 with a degree of up movement of 30% and down movement of 10% for each year. The firm issues a specified senior (B_S) with the face value (F_S) of $300 and a term of 3 years, and a specified junior bond (B_J) with the face value (F_J) of $400 and a term of 3 years. The risk-free annual rate is 10%. Please find the fair premiums of senior bond, junior bond and equity (E) by the binomial pricing model. At terminal day, they have following terminal payoffs:

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