Sample End Term Exam

Financial Mathematics (End Term Exam)

Prof. Mahendra Mehta

Part 1 – 40 Marks

Open Book, No Laptops, No Internet, ONLY Calculators are allowed. Please show all your steps in your computation. Using Financial Calculator to compute the values will not fetch a high grade.

You are a bond portfolio manager and have a thousand each of the following bonds in your portfolio

1) Compute the bond price, duration and convexity of the following bonds

	COUPON	MATURITY	YTM
Bond A	5% Annual	5 Years	7%
Bond B	12% Semi-Annual	3 Years	5%
Bond C	10% Quarterly	2 Years	3%

Face Value or Par Value of each bond = $ 1,000

2) Calculate the Duration of a Portfolio which has a 1,000 bonds of all the 3 types above

3) Your chief economist forecasts interest rates to rise. As a fund manager, which of the bonds will you sell from your portfolio in response to that forecast?

Part 2 – 60 Marks

Open Book, laptops and calculators allowed but no internet connection allowed. Please show all the steps in your computation. You are required to submit your excel spreadsheet as the answer to this question.

Price the following European style PUT option using a Binomial Tree with 10 discreet time periods:

· Stock Price today = 100

· Strike Price = 90

· Time to maturity = 1 Year

· Volatility = 20%

· Risk Free Interest Rate = 2%

PART TWO - OPTIONAL QUESTION: Extend the binomial tree to 200 steps and calculate the price of the above option using the binomial tree. Also calculate the value of the option using Black Scholes model and check whether the 2 prices converge.