Fin Engin. HW#4 1) Two corporate bonds (from two different issuers) were issued at par (i.e., priced at notional value at their issuance) with notional $1000 and 3% and 7% coupon paid annually at year...

Answering attached 5 questions with step by step answers


Fin Engin. HW#4 1) Two corporate bonds (from two different issuers) were issued at par (i.e., priced at notional value at their issuance) 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 $1020.78, what are their internal yield of return (YTM)? (3) Can you speculate what happened to the two companies since they issued their bonds? Assume the risk free interest rate curve stayed at about the same level since the issuance of both bonds. 2) 2) The 6, 12, 18, 24 month risk free zero rates (semi-annual compounding) are 0.4%, 0.8%, 1.2%, 1.6% respectively. What is the equilibrium swap rate for a two year interest rate swap referenced to the above zero curve with semi-annual interest payment exchange? Ignore counter party credit risk. 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) 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 the put option? 5) A stock is currently traded at 80. The annualized volatility is 30%. 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 CRR binomial tree. (2) What if the put is American? Price it using a two step CRR binomial tree.