1. © K. Cuthbertson and D. Nitzsche Figures for Chapter 23 VaR : MAPPING CASH FLOWS (Financial Engineering : Derivatives and Risk Management)

2. © K. Cuthbertson and D. Nitzsche Figure 23.1 : RiskMetrics : Mapping cash flows 5 $ 100 m RM Cash Flow 6 7 5 7 Actual Cash Flow

3. © K. Cuthbertson and D. Nitzsche Figure 23.2 : Sell 6 month x 12 month FRA : actual cash flows 06m12m Lend $1m for 6 months Receipt from money lent at t = 6 months f 6,12

4. © K. Cuthbertson and D. Nitzsche Figure 23.3 : Sell 6 month x 12 month FRA : synthetic cash flows 06m12m Repay 6-month loan Receipt at 12-months from lending at t = 0 f 6,12 Lend (long) $969,121 at 12-month rate Borrow (short) $969,121 at 6-month rate

5. © K. Cuthbertson and D. Nitzsche Figure 23.4 : Cash flows FRN between payment dates r 01 0123Timet Qr 01 Qf 12 Q(1+f 23 ) f 12 f 23 r* 1-t r* 2-t r* 3-t Note : If t = 0.25 years into the swap, then 1-t = 0.75 years, 2-t = 1.75 years and 3-t = 2.75 years.

6. © K. Cuthbertson and D. Nitzsche Figure 23.5 : Equivalent cash flows FRN between payment dates 0123 Time t Q(1 + r 01 ) r 01

7. © K. Cuthbertson and D. Nitzsche Figure 23.6 : Cash flows in forward contract and synthetic 0 1 3.) Lend (go long) at r f Euros = 10e -rf(T-t) 2.) Borrow (go short) USD = $10.95m = 10 Fe -rd(T-t) = 10 Se -rf(T-t) 4.) Euro 10m 1.) USD 11.61m F = 1.161 ($ per euro) Note : We have used F = S exp [(r d -r f )(T-t)]