Derv#

Question 1

CDS Payout Ratio

CDS Payout Amt

Answer 1

1 - %recovery rate

Payout ratio)*(notional

Question 2

Probability of survival
Conditional probability of survival
Probability of survival through t

Answer 2

Prob of survival = 100% - hazard rate

Probability of survival through t = (prob of survival)*(conditional prob of survival)

Question 3

Probability of default

Answer 3

= 1 - Prob of survival

Question 4

Upfront pmt

Answer 4

= pv(protection leg) - PV(prem leg)

If result >zero, buyer pays seller
If result

Question 5

Upfront premium

Answer 5

= PV(credit spread) - PV(fixed coupon)

= approx (credit spread - fixed coupon)*(duration)

Question 6

Price of CDS in currency per 100 par

Answer 6

100 - (upfront prem %)

Question 7

Profit for the buyer of protection

Answer 7

= approx (chg spread)(duration)(notional)

Question 8

%chg in CDS price

Answer 8

(Chg spread)*(duration)

Question 9

2 yr floor =

Answer 9

1yr put option on LIBOR(floorlet) + 2yr put option on LIBOR (floorlet)

Question 10

Long cap

Long floor

Answer 10

Long cap = portfolio of long put

Long floor = portfolio of long call

Question 11

Cap payoff

Floor payoff

Answer 11

Cap Periodic pmt = max(0, (notional principal)(index rate - cap rate)(actual days/360))

Floor Periodic pmt = max(0, (notional principal)(floor rate - index rate)(actual days/360))

Question 12

Delta (hedge ratio)
# of shares per option

Answer 12

n = [(C+)-(C-)]/[(S+)-(S-)]

Question 13

Delta-neutral Portfolio

Answer 13

rf combination of long stock & short call where the number of calls to sell = (# of shares hedged)/(delta call option)

Question 14

IR caplet

Call option on IR

Answer 14

expiration value of caplet = max(0, 1yr rate - cap rate)*notional)/(1+1yr rate)

Question 15

IR floorlet

Put option on IR

Answer 15

expiration value of floorlet = max(0, floor rate - 1yr rate)*notional)/(1+1yr rate)

Question 16

BSM estimates

Answer 16

N(d1) = delta
chg(call) ~ N(d1)(chg(So))
chg(put) ~ [N(D1)-1](chg(So))

Question 17

Put Call Parity for underlyings with CFs

Answer 17

(Co) + (X/(1+rf)^t) = (Po) + (So - PVCF)

Question 18

Put Call Parity for options on forwards or futures

Answer 18

(Co) + (X-Ft)/((1+rf)^t) = (Po)

Ft = (Co-Po)*(1+rf)^t + X

Question 19

Put Call Parity

Answer 19

(Co) + (X/(1+rf)^t) = (Po) + (So)

Co) + (X/(e^(rf*t)) = (Po) + (So