5. Derivatives Flashcards
Derivative Types
- Forward / Future
- Swaps
- Options (call, put)
- FRA
Benefits of Usage
- Information on Price (discovery)
- Risk Management
- Lower transaction costs
Long / Short (concept)
Long = Buy Short = Sell
Synthetic FRA (90d FRA on 180 LIBOR)
Borrow for 270d (180+90), lend for 90d
Future v. Forward (Difference)
-Futures: standardized, traded in stock exchange, margin deposit and margin maintainance (@ initial requirement)
Daily Settlement Price
- Avg of prices during the last period of trading, which determines margin
Value v. Price
Price: F0 discounted @ Rf interest rate
Swap
Plain Vanilla: fixed for floating rate
Series of FRAs with fixed rate (dif. maturities), equal value
CDS
- Measured in bps
- PMT over a notional (n = 6 months)
In The Money (concept)
Call: (S - X) > 0
Put: (X - S) > 0
Moneyness independ of premium
Breakeven depend on premium paid
Premium and Intrinsic Value / Time Value
Premium = Intrinsic (Exercise Value) + Time Value
Time Value = 0 @ expiration
Exercise Value = Max between 0 and (S - X) or (X - S) = In the Money
Gains / Losses (Put / Call)
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)
Price of Derivative (Fwd, Swap)
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
Replication (concept)
Position in the asset + derivative hedge = risk-free gain
Derivative Value (formula)
V = S0 - F0 / (1+ Rf)^T
Vt(T) = St + PVcost - PVBenefit - F0 / (1+Rf)^T
Factors influencing Option Value
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
Put-Call Parity
s + p = c + x / (1+Rf)^T
s + p = protective put
Protective Put (formula)
Formula: (s + p) = (x + c)
It means that it pays off the same thing as a risk-free bond + long call
Fiduciary Call (formula)
(c + x) = (s + p)
“bomdcal”
Binomial Model (step by step)
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
