Derivatives

CFA_LV2_Deri_F.hwp

 

 

 

 

 

Derivatives

 

[ Forward Markets and Contracts ]

 

○ Forward Price

- P = 무위험차입 → 기초자산 매입 → + 비용(Rf이자, 보관), - 수익(채권이자, 배당)

- V = PV of ( new P - old P)

 

○ 2×3 FRA

- 2개월 후 1개월(3-2)간 금리

- libor, 360 base → 금리 일할계산

 

[ Futures Markets and Contracts ]

 

○ Futures vs. Forward

- futures : MTM cash flow → reinvestment

correlation between underlying asset value and interest rates	Investors
positive	long futures
zero	no preference
negative	long forward

 

○ Backwardation vs. Contango

- backwardation : expected spot > futures, positive roll yield

- contango : expected spot < futures, negative roll yield

○ T-bill and T-bond

	spot price	futures price
Euro dollar	annualized Libor	100 - annualized 90 day Libor
T-bill	annualized discount rate	100 - annualized 90 day discount rate
T-bond	32nd, 액면가 × (95 + 5/32)% = clean price

 

○ 표준선물 가격

- FP = [bond price × (1+Rf)T - FVC] × 1 / CF

- FVC : future value of coupon payment, CF : conversion factor

 

[ Option Markets and Contracts ]

 

○ Put-call parity

-

- protective put = fiduciary call

 

○ Black-Scholes-Merton model

- the price of the underlying asset follows a lognormal distribution

- the (continuous) risk-free rate si constant and known

- the volatility of the underlying asset is constant and known. option values depend on the volatility of the price of the underlying asset or interest rate.

- markets are "frictionless." there are no taxes, no transaction costs, and no restrictions on short sales or the use of short-sale proceeds.

- the underlying asset has no cash flow, such as dividends or coupon payments.

- the options valued are European options, which can only be exercised at maturity.

 

○ Binomial model

- D = size of down move = 1 / U (size of up move)

- πD = risk-neutral probability of an up-move = (1 + Rf - D) / (U - D)

 

○ Greek

sensitivity factor	input	call / put
Delta	asset price	positive / negative
Gamma	delta	positive / positive
Vega	volatility	positive / positive
Rho	risk-free rate	positive / negative
Theta	time to expiration	negative / usually negative
	exercise price	negative / positive

 

[ Swap Markets and Contracts ]

 

○ Periodic payment, C

- C = (1 - 원금현가) / ∑현가계수

- 연율 환산 시, × 2(semi-annual) or × 4(quarter)

 

○ Credit risk

- highest in the middle of swap term

- payment risk 감소, but 금리변동성 risk 증가

- CRS : higher in little later

 

[ Interest Rate Derivative Instruments ]

 

○ Cap & Floor

- long cap = long put options on fixed-income security prices

- long floor = long call options on fixed-income security prices

 

○ Long interest rate collar

- long collar = short floor + long cap

- short floor를 통해 자금 조달, 금리 상승 위험 헤지

 

[ Credit Default Swap ]

 

○ CDS credit events

- bankruptcy, failure to pay, restructuring

- moratorium (지급 유예), repudiation (지급 거절)

 

○ Upfront premium

- ( CDS spread - CDS coupon ) × duration

- CDS price = 100 - upfront premium