Financial Derivatives

Forward and Futures

pricing:
F(t, T) = S(t) e ^ (r + u - d -y) (T-t)
where T: expiration date
r : risk free rate
u : storage cost
d : dividend yield
y : convenience yield

OTC central clearing to lower counterparty risk, such as London clearing house (LCH)

futures contracts are settled by cash settlement
futures contracts are closed  by entering into an offsetting position relative to your original position

Interest Rate Forward

notation:
2f1 - 1 year from now, 6 month rate
14f6 - 7 year from now, 3 year rate

By the principle of no arbitrage,
 (1+r1/2)(1+1f1 /2) = (1+r2/2)2, solve for 1f1
r1: 6 month spot
r2: 1 year spot

Interest Rate Swap

interest rate is implied in swap
USD/THB spot
USD LIBOR
# of days
swap point = fwd - spot
Σ PV (fixed) = Σ PV(floating)

money market rate, and bond rate affect swap rate

bank use PV01 to calculate risk
if gap > threshold, bank charge more

DV01 or PVBP
- 30 yr bond with 5.5% coupon
at yield of 5.5%, price = 100
at yield of 5.51%, price = 99.8540
DV01 = 0.146% of par
or DV01(per $1 mm par) = $1460

** take note **
- PV01 is change in market value from bumping the coupon rate by 1 bp
- DV01 is the change in market value for a 1 bp parallel shift of the yield curve

**hedge bond investment with bond futures
- use DV01
DV01 of 6 year bond with coupon of 5.5%: 712.5 per $1million par value
DV01 of 6 year bond with coupon of 5.0%: 613.1 per $1million par value
- the hedge ratio  (futures contract to sell) of 6 year bond investment against interest rate risk is
  hedge ratio = 712.5/613.1

Cross Currency Swap

- agreement between two parties to exchange principal and interest payments in two currencies over specified period
- may have or my not have initial principal exchange
- interest payments are usually not netted

basis swap (floating vs floating)

FX Forward

EUR/USD  ; ieur < iusd
EUR/USD forward, EUR appreciate
=> swap point +ve
=> EUR/USD > spot

AUD/USD  ; iaud > iusd
AUD/USD forward, AUD depreciate

=> swap point -ve
=> AUD/USD < spot

Case study:
Delox imports machine from Japan. Its revenue is in EUR, while its expense is in JPY. It expects to pay JPY 1000 million in 6 months. How to manage its FX risk?
Ans: one way is to buy JPY forward
EURJPY spot rate 129.45
6 month EURJPY forward rate 128.26

forward: bank charge bid offer spread
swap: bank will not charge bid offer spread