# Modeling VaR of Swaps. Dr Nitin Singh IIM Indore (India)

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1 Modeling VaR of Swaps Dr Nitin Singh IIM Indore (India)

2 Modeling VaR of application Palisade Corporation

3 Overview of Presentation Swaps Interest Rate Swap Structure and Uses The Swap Curve Valuation of IR Swap Bond Viewpoint & as PV of Forward Rate VaR Simulation to find VaR for swaps Implications

4 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

5 Interest Rate Swap An agreement between two parties to exchange a series of interest payments, one for another. Typically: One floating rate (LIBOR, T-Bill, Federal Funds) Other fixed rate (Based on LT rates: T-Bond)

6 Interest Rate Swap Notional Principal Size of Payment Example 8% on 10m quarterly Amortization = (1/4) m = 200k Parties in Swap: Fixed-rate Payer Floating-Rate Payer

7 Interest Rate Swap Why Swaps Work? People have opposite positions

8 Interest rate swap swapping fixed for floating or vice- versa Interest rate floating fixed days

9 Interest Rate Swap Swaps can be used for: Hedging against interest rates Major players: Citigroup, JP Morgan, bankers Trust, First Chicago etc.

10 Interest Rate Swap Why Swaps Work? Market access Cheap to eliminate risk Arose from: S&L exposure in late 1970s Lent fixed rate Took ST variable rates

11 Interest Rate Swap example An agreement by Intel to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for two years on a notional principal of \$10 million

12 Cash Flows to Intel LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Sept 2, % March 2, % Sept 2, % March 2, % Sept 2, %

13 Cash Flow Diagram of Swap + Pay Fixed at 5% - t 0 t 1 t 2 t 3 t 4 Receive Floating at LIBOR Payment at t i, fixed at t i-1 + Net Cash exchanged -

14 Typical Uses of an Interest Rate Swap Converting a liability from fixed rate to floating rate floating rate to fixed rate Six-month LIBOR is a short-term AA borrowing rate Converting an investment from fixed rate to floating rate floating rate to fixed rate

15 Swap Curve March 01, 2007

16 The Comparative Advantage of Swaps Ability of Counterparties to take advantage of their comparative advantage in the Debt Markets Borrowers with different credit quality will have comparative advantage in fixed or floating Markets As a result a company may Borrow Fixed when it wants Floating Borrow Floating when it wants Fixed..It can Adjust the result through the Swap Market

17 Valuation of swaps in terms of Bonds Notional, yields, floating and fixed payments are known Procedure. Effective swaps to be computed

18 discounting to present values Dp = r 6 p 0 At date t = 6, the floating leg will pay r6% which is discounted back to t = 0 by using the six-month zero price at t = 0, which is p0.

19 Volatility in yield

20 forward rates f 0 (6,12) 2 f + 0(0,12) 1 2 = 2 1 f (0,6) At date t = 0, f 0 (0,12) six month forward rate that will prevail from t = 6 to t = 12

21 present value at t = 0 of receiving at t = 12 PV = 12 f 0 6,12) * ( P 12 As floating leg will reset to at t = 6 the counter party will actually pay this amount at t = 12.

22 Set PV of fixed equal to PV of floating x T PVt, t+ 1 o = T t PV x = effective swap rate PV t = present value of all floating payments t= time period (maturity) PV t,t+1 = present value of fixed leg payments t

23 @Risk model file

24 Case illustration Maturity Yield Zero Prices Forward Rates

25 Valuation of Swaps t = 6 t = 12 t = 18 t = 24 Sum Floating payments 5.50% 5.90% 6.30% 7.10% Zero prices PV (float) Total: Swap rate: ( )/ = %

26 Value at Risk Measuring risk in swaps

27 Value at Risk Quantifies risk which captures the odds of losing money What is the probability that an investor will lose money in a worst case scenario? How much (amount) can be lost in a worst case scenario?

28 VaR Monte Carlo Simulation it has a confidence level through which the analyst can estimate VaR with a certain degree of confidence An investor in a swap transaction has a potential to lose money on his transaction but what is the most that investor can (with a given confidence level) expect to lose over the next time period? VaR = 1.645σ + ( p µ ) Based on the fact that the 5%- quantile of a normal distribution always occurs standard deviations below its mean

29 Simulation to find VaR Simulation used to generate multiple interest rate scenarios and compute the value that could be potentially lost..defined by three basic elements confidence level, time period and the value that could be potentially lost

30 Simulation Simulation model developed for future bond yields multiple trials though the model Simulation length was kept to 100 Replicated the simulation 50 times

31 VaR at 7.56 % of notional amount

32 @Risk output

33 Conclusions A spreadsheet model to value interest rates VaR at 7.56% of notional amount indicates that the investor is likely (5% chances) to lose this % of its invested amount An easy to use model which can be modified to do similar analysis including credit and currency risk

34 Questions..

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