Questions: 1) Two corporate bonds (from two different issuers) with notional $1000 and 3% and 7% coupon paid annually at year 1, 2, 3, 4 and 5, have 5 year remaining before they mature. The current...

Answering attached 5 questions with calculations


Questions: 1) Two corporate bonds (from two different issuers) with notional $1000 and 3% and 7% coupon paid annually at year 1, 2, 3, 4 and 5, have 5 year remaining before they mature. The current risk free discount curve is 2% flat, annual compounding. (1) what is the present value of these bonds under the risk free discount curve? (2) The 3% bond is traded at $817.94, the 7% bond is traded at $989.82, what are their internal yield of return (YTM)? (3) Can you speculate what happened to the two companies since they issued their bonds? 2) 2) An interest rate swap with $1M notional that pays 3% fixed rate and receives LIBOR has 2 year to mature. It exchanges cash flow every 6 month. The current 6 month LIBOR is set at 2%. The 6 – 12 month, and 12 – 18 month forward LIBOR are known to be 2.8% and 3.5% respectively. The OIS rate is 1.8% (continuous compounding) flat. The swap is traded at $35,107.74. What is the 18 – 24 month forward LIBOR rate? 3) 3) A client asked 3 financial institutions (A, B and C) to price a 10 year forward contract to buy stock S that currently traded at $100. The company pays yearly dividend (once per year). The last dividend was paid 6 month ago at $5 per share. It is expected to pay the same amount 6 month from now as well. The risk free interest rate is 3% (continuous compounding) flat. Institution A priced the forward by assuming the stock will pay $5 dividend every 12 month starting 6 month from now; B priced it by assuming the stock pays 5% continuous dividend yield throughout the life of the forward; Trader at C believes in the next two years the company will pay $5 annual dividend but not sure if the company will adjust dividend thereafter as stock price changes. Furthermore she thinks that continuous dividend yield is not a good approximation. Hence the trader at C priced the forward with the assumption that the stock will pay $5 dividend at 6th and 18th month, and 5% proportional dividend every 12 month thereafter (i.e., at 30th month the company pays dividend equals to 5% of its then stock price. This payment will be repeated every 12 month before maturity). Assume the continuous dividend yield and the discrete annual proportional dividends are reinvested in the stock. (1) What is the forward prices institution A gave to the client? (2) What is the forward prices institution B sent to the client? (3) What is the forward prices institution C sent to the client? Explain how she calculated it. 4) 4) A 3 year European call and a 3 year European put on a dividend paying stock are traded at $22.13 and $21.85 respectively. Both options have the same strike $102. The risk free rate is 4% (continuous compounding). Current stock price is $100 and pays 3% continuous dividend yield. (1) Are these options fairly priced? If not, what trade can you put on to monetize the miss pricing? (2) Assume that the call price is fairly priced, what should be the fair price for theput option? 5) 5) A stock is currently traded at 80. In a binomial world it can only go up to 10% with 65% probability or come down 10% with 35% probability. The risk free interest rate is 2% (continuous compounding). (1) What is the value of a 1 year European put option with strike = 82? Present your answer in both single step and two step binomial tree. (2) What if the put is American? Price it using a two step binomial tree.