5. Derivatives

Question 1

Derivative Types

Answer 1

• Forward / Future
• Swaps
• Options (call, put)
• FRA

Question 2

Benefits of Usage

Answer 2

• Information on Price (discovery)
• Risk Management
• Lower transaction costs

Question 3

Long / Short (concept)

Answer 3

Long = Buy
Short = Sell

Question 4

Synthetic FRA (90d FRA on 180 LIBOR)

Answer 4

Borrow for 270d (180+90), lend for 90d

Question 5

Future v. Forward (Difference)

Answer 5

-Futures: standardized, traded in stock exchange, margin deposit and margin maintainance (@ initial requirement)

Question 6

Daily Settlement Price

Answer 6

• Avg of prices during the last period of trading, which determines margin

Question 7

Value v. Price

Answer 7

Price: F0 discounted @ Rf interest rate

Question 8

Swap

Answer 8

Plain Vanilla: fixed for floating rate

Series of FRAs with fixed rate (dif. maturities), equal value

Question 9

CDS

Answer 9

• Measured in bps

- PMT over a notional (n = 6 months)

Question 10

In The Money (concept)

Answer 10

Call: (S - X) > 0
Put: (X - S) > 0

Moneyness independ of premium
Breakeven depend on premium paid

Question 11

Premium and Intrinsic Value / Time Value

Answer 11

Premium = Intrinsic (Exercise Value) + Time Value

Time Value = 0 @ expiration

Exercise Value = Max between 0 and (S - X) or (X - S) = In the Money

Question 12

Gains / Losses (Put / Call)

Answer 12

Calls: trava a perda no prêmio

Put: ganho máximo é o strike, se o preço do ativo for zero (0)

P/ quem tá short, o prêmio sempre é o maior ganho possível (caso a opção vire pó)

Question 13

Price of Derivative (Fwd, Swap)

Answer 13

Fwd price: price @ which the parties agree to buy/sell the underlying in the future

Swap / FRA: long always receive floating; so the price is the fixed rate

Question 14

Replication (concept)

Answer 14

Position in the asset + derivative hedge = risk-free gain

Question 15

Derivative Value (formula)

Answer 15

V = S0 - F0 / (1+ Rf)^T

Vt(T) = St + PVcost - PVBenefit - F0 / (1+Rf)^T

Question 16

Factors influencing Option Value

Answer 16

Inverse Relation:
↑ Asset Price = ↑ Call / ↓ Put
↑ Risk-Free = ↑ Call / ↓ Put (check put-call parity)
↑ Dividends = ↓ Call / ↑ Put

Direct Relation:
↑ Time = ↑ Call / ↑ Put
↑ Vol = ↑ Call / ↑ Put

Question 17

Put-Call Parity

Answer 17

s + p = c + x / (1+Rf)^T

s + p = protective put

Question 18

Protective Put (formula)

Answer 18

Formula: (s + p) = (x + c)

It means that it pays off the same thing as a risk-free bond + long call

Question 19

Fiduciary Call (formula)

Answer 19

(c + x) = (s + p)

“bomdcal”

Question 20

Binomial Model (step by step)

Answer 20

Steps:
a. Data: Size Up = 1.15
b. Find Size Down = (1 / Prob Up) = 0.87
Rf = 3%

c. Find Rf Probability by formula
(1 + Rf) - D / (U - D)
d. Prob down = (1 - Result of Formula)
= 57% e 43%

e. Calculate Payoffs if Up / Down
(i) Up: (S0 * Movement Size )
(ii) Down: (S0 * Movement Size)

Final Step
Sum = (% Up * Payoff Up) + (%Down * Payoff Down)

Sum = 57%*Payoff Up + 43%Payoff Down