R.39 Pricing and Valuation of Forward Commitments

Question 1

1. Forward price (w/out carry cost or benefits)
2. Value of Forward contract (long position) (w/out carry cost or benefits)
3. Forward price with discrete CFs
4. Forward price with continuous CFs
5. Value of Forward contract (long position) with cash flows

Answer 1

Question 2

FRAs

What is it?

Steps to solve?

Answer 2

(FRA) is an over-the-counter (OTC) forward contract (not standardized) in which the underlying is an interest rate on a deposit. FRA involves two counterparties:

• fixed receiver (short) and the
• floating receiver (long).
  
  • ​gains when LIBOR rises

Question 3

Price of bond futures contract when accrued interest not included in bond price quote

Price of currency forward

Value of currency forward (long position)

Answer 3

Question 4

FS1 Futures Treasury Bond contract

Pricing/Valuation of Fwd Commitments

Futures contracts - Treasury Bond

• Describe/compare features/formula

Answer 4

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 5

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 5

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)]