Derivatives

Question 1

FS1 Futures Treasury Bond contract

Pricing/Valuation of Fwd Commitments

Futures contracts - Treasury Bond

• Describe/compare features/formula

Answer 1

Futures Price:

FP = [(full price)(1 + R_f)^T - AI_T - FVC]

Quoted Futures Price:

QFP = FP / CvF

QFP = [(full price)(1 + R_f)^T - AI_T - FVC] x ( 1 / CvF )

Futures Contracts w/ Treasury Bond

• Must adjust fwd pricing formula to account for short delivery option
• Each deliverable bond assigned Conversion Factor (CvF) to adjust settlement pmt for delivery of higher or lower cpn bonds
• Use CvF for cheapest-to-deliver (CTD) bond

Note - Kaplan books uses CF in place of my CvF for term. I’m choosing to use CF as cashflow for all divs, cpns, etc.

Question 2

FS1 - Fwd contracts w/ CF

Pricing/Valuing Fwd Commitments

Describe/Compare

Pricing/Valuing Fwd Contracts with Cash Flows

(same for dividends, coupons, etc)

• FP = ?
• V = ?

Answer 2

FP = (S₀ - PVCF) x (1 + R_f)^T

= S₀ x (1 + R_f)^T - FVCF

V_t (long position) = (S_t - PVCF_t) - [FP / (1+R_f)^(T-t)]

Question 3

Cash & Carry

Pricing/Valuing Forward Committments

Cash and Carry

(forward contact model example)

Answer 3

Question 4

Fwd Contract Valuation and Price (cost-of-carry model)

Pricing and Valuing Forward Commitments

Fwd contract price (cost-of-carry model)?

Fwd contract valuation?

Answer 4

Price

FP = S₀ x (1 + R_f)^T

S₀ = FP / (1+R_f)^T

Value

= S_t - [ FP / (1+R_f)^T-t

Question 5

PVFC - Equity Index pricing forward contracts

Pricing & Valuation of Forward Commitments

Describe/Compare

price of an equity index forward contract with continuous dividends

Answer 5

FS1

FP (equity ix) = S₀ x e^{(Rf^c - g^c) x T}

^{Focus on above formula. Easier to remember. (Rf^c - g^c) is the net cost to carry (Rf rate minus dividend yield). Calcuate the raised e factors first then hit} e^x

Question 6

Futures price for a bond

Pricing & Valuation of Fwd Commitments

price of a bond futures contract:

Answer 6

FP

Question 7

price of a currency forward contract?

value of a currency forward contract?

Answer 7

Question 8

• breakeven price analytics
• volatility needed to break even

Answer 8

Question 9

• put-call parity
• put-call parity when stock pays div

Answer 9

Question 10

BSM model

Answer 10

Question 11

change in option value

Answer 11

Question 12

dynamic hedging

Answer 12

Question 13

Option value using artbitrage-free pricing portfolio

Answer 13

Question 14

price and value for a currency forward contract (continuous time)

Answer 14

Question 15

probability of movements in binomial stock tree:

• up-move
• down-move

Answer 15

Question 16

swap fixed rate

Answer 16

Question 17

value of plain vanilla interest rate swap (to payer) after inception

Answer 17

Question 18

value prior to expiration of a forward contract on a coupon-paying bond:

Answer 18

Question 19

Futures arbitrage example

Pricing & Valuation of Forward Commitments

Describe/compare

See slide example

Answer 19

Question 20

FRA - Forward Rate Agreement

Pricing & Valuing Fwd Comittments

Describe/Compare

Forward Rate Agreements (FRA)

• Describe basics?
• What is “2x3” FRA?

Answer 20

Describe FRAs

• Agreement to borrow (long) or lend (short) in future
• Based on LIBOR w/ #days/360

2x3 FRA

• Fixed rate starts today and FRA starts today
• Think of both numbers starting from today to specify:
  
  • when he FRA expires and floating rate beings (2mo from today)
  • when notional borrowing/lending ends (3mo from today) and difference is paid to winner

Question 21

FRA pricing example

Pricing/Valuing Forward Comittments

Calculate/Interpret

Pricing a FRA

Answer 21

• need to calculate implied forward rate to solve
• implied forward rates needs Bracketing Rates!
• must un-annualize the bracket spot rates and the find Implifed forward rate for 60-days
• Insert long and short rates into formula for IFR and then multiply by 360/60 to annualize the 60-day spot rate 30-days from now.
  
  • FR₆₀ = [(1 + Long) / (1 + Short) - 1] x ( ³⁶⁰/_days )
    *

Question 22

FRA - Valuing at Maturity

P/V Fwd Commits

Calculate/Interpret

Valuing an FRA at Maturity

Answer 22

Question 23

Currency Swaps - describe/compare

P/V Fwd Commit

Currency Swaps

• priced w/?
• principal?
• periodic payments?

Answer 23

• Interest rates used to price currency swaps are simply swap rates calculated from each currency’s term structure.
• Currency swaps exchange principal [at initiation’s F(x) rate] b/c participants actually need other currency
  
  • Other swaps (equity rate, etc) d__o not exchange principal
• Periodic payments based on each currency’s fixed rate
• know this slide:

Question 24

Currency Swap Valuation