Derivatives Formulas

Question 1

Forward and Futures Price: Cost-of-Carry Model

Answer 1

FP = S0 x (1 + Rf)^T

OR

S0 = FP / (1 + Rf)^T

Question 2

Value of a Forward Contract

Answer 2

Remember: if they are asking for short, just make it a MINUS

THINK: spot price - PV of FP

Question 4

Price of an equity forward contract OR coupon-paying bond

Answer 4

FPe = (S0 - PVD) x (1 + Rf)^T

PVD = present value of dividends

Example: 6% semi-annual cpoun, S = 1,071.77. Next dividend in 183 days. Rf = 5%, forward contract matures in 195 days

PVC = $30 / (1.05)^183/365 = $29.28

FP = ($1,071.77 − $29.28) × (1.05)^195 / 365 = $1,070.02

Question 5

Price of Equity Index Forward Continuous Dividends

Answer 5

FPindex = S0 x e^(Rf -dy) * T

Question 6

Forward Rate agreement (FRA) Pricing

Answer 6

Step 1: De-annualize rates: r * (days/360)

Step 2: Price the FRA: [(1 + long) / (1 + short)] - 1

Step 3: annualize: (360/days)

Example: 1 x 3 for which 30-day rate is 2.4%, 60-day is 2.8%, 90-day is 3.0%

unannualized 30-day rate is: 0.024 x 30/360 = 0.002
unannualized 90-day rate is: 0.03 x 90/360 = 0.0075
(1.0075 / 1.002) - 1 = .005489
.005489 * (360/60) = 3.3%

Question 7

Value of a Currency Forwards

Answer 7

V = [St / (1 + Rforeign) ^T-t] - [FP / (1 + Rdomestic) ^T-t]

priced based on covered interest rate parity

Question 8

Value of a Equity Forward

Value of Fixed Income Forward

Answer 8

Equity: [St - PVDt] - [FP / (1 + Rf)^T-t]

Fixed Income: [St - PVCt] - [FP / (1 + Rf)^T-t]

Question 9

Price of a Currency Forward

Answer 9

FP = S0 * (1 + Rdomestic)^T / (1 + Rforeign)^T