1. Interest Rates R. Srinivasan

2. Introduction Interest rates are the back-bone of valuation of virtually all financial instruments, especially the derivatives.

3. Types of Rates Treasury rates –T Bills, T Bonds are instruments used by Government to borrow in its own currency –Totally risk-free, because it is assumed that there are no chance of government defaulting in its commitment. LIBOR rates –Rates at which one bank is prepared to wholesale lending to another bank. –Accepted creditworthiness/rating is AA, which is considered relatively risk-free –But traders prefer to treat LIBOR as proxy for risk-free over Treasury rates, due to a number of tax and regulatory issues causing the T. Rates to be kept artificially low. –LIBID rates are at which banks accept deposits from other banks –LIBOR & LIBID are traded in the Eurocurrency Market, which is outside the control of any single government.

4. Types of Rates Repo rates –Investment dealer sells (owned) securities at some price with an agreement to buy it back (repurchase) later at a higher price. The (interest) spread between buying – selling is called the repo rate. –In case of default from either side, the seller keeps the cash and buyer keeps the securities, thus eliminating any credit risk. –Types: Overnight repo rate and term-repo rate.

5. Measurement of Interest Rates The compounding frequency used for an interest rate is the unit of measurement The quarterly compounding and annual compounding are two different units of measurement i.e., unequal. Annual compounding = 1.If compounded m times per annum =

6. Continuous Compounding 2.As per limits theorem as the compounding frequency, m ∞, it is called continuous compounding and an amount A invested grows with And discounting is done with

7. Conversion Formula Define R c : continuously compounded rate R m : same rate with compounding m times per year From equations at (1) & (2), we get because, if y = ln x, then x = e y Hence given R c, we can find out R m and vice versa. 3. 4.

8. QUESTIONS 1)What rate of interest with continuous compounding is equivalent to 15% p.a. with monthly compounding? 2)A deposit account pays 12% p.a. with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a Rs. 10,000 deposit?

9. QUESTIONS 1)What rate of interest with continuous compounding is equivalent to 15% p.a. with monthly compounding? 2)A deposit account pays 12% p.a. with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a Rs. 10,000 deposit? RmRm 15.00%Equivalent R c # COMPOUNDING1214.907% RcRc 12.00%Equivalent R m # COMPOUNDING4 12.182%

10. Zero Rates A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T. There are no interim coupons. Example –5-year zero rate with continuous compounding is 5% p.a. –Face Value of Bond = Rs. 100/- Maturity Value = 100 x e 0.05 x 5 = Rs. 128.40