Calculate the cash settlement at the start of the period (PV) for a FRA with notional N = 100,000,000, fixed rate 2.24299% (quarterly actual/360), realized floating MRR = 2.15%, period 90/360, if the net at end-of-period would be (MRR - fixed) * N * period = (2.15% - 2.24299%)*N*(90/360). What is the approximate present value at period start using discounting by realized MRR?
Explanation
FRA net payment is discounted to start of period using realized MRR; compute end net then discount by (1 + MRR/4) for quarter example.
Other questions
Consider a non-dividend-paying stock with current spot price S0 = 100 and an annual discrete risk-free rate r = 5%. What is the no-arbitrage one-year forward price F0(1) under discrete compounding?
A commodity spot price S0 = 1,000 has a known storage cost of 10 payable at maturity in one year. The risk-free rate is 4% (discrete). Assuming no other income, what is the no-arbitrage forward price F0(1)?
An equity index has spot level S0 = 10,000, expected continuous dividend yield i = 2% (continuous), and continuous risk-free rate r = 5%. What is the one-year forward price under continuous compounding?
You observe a spot gold price S0 = 1,770 and a three-month forward quote of F0 = 1,792.13. If annual discrete risk-free rate is 2% and storage cost is zero, is there an arbitrage opportunity and what trade yields a riskless profit?
An investor can borrow at the continuous risk-free rate rd = 0.2% and lend in AUD at rf = 0.05% (six-month rates). The spot AUD/USD is 1.3335. What is the six-month FX forward AUD/USD? Use continuous compounding.
Given spot S0 = 50, observed six-month forward F0(0.5) = 52.50, and annual discrete risk-free rate r = 4% (annual). Asset has no carry. What is the arbitrage profit per unit if you buy spot and sell forward for six months? (Compute profit using discrete compounding.)
A stock pays a known dividend of 0.30 in three months and again at six months. Spot S0 = 50, r = 5% (annual). What is the forward price in six months F0(0.5)?
If benefits of owning an underlying (convenience yield or dividends) exceed the carrying costs including opportunity cost r, what is the relationship between forward price F0(T) and spot S0?
An investor observes S0 = 19.50 MXN/USD, six-month MXN rate 4.0%, six-month USD rate 0.25%. What is the no-arbitrage six-month MXN/USD forward? Use continuous compounding.
A one-year zero rate z1 = 2.5% and a two-year zero rate z2 is unknown. A two-year annual coupon bond pays 3% and trades at PV = 98. Assuming par 100 face, solve z2 if the bond price is 98.275 and z1 = 2.396% (use discrete compounding). Which approximate z2 matches the bond price scenario in the chapter?
Given zero rates z1 = 2.3960% and z2 = 3.4197%, find the one-year forward rate starting one year from now (IFR1,1) under discrete compounding.
A trader can invest 100 for one year at z1 = 2.396% then reinvest the proceeds for one year at the implied forward IFR1,1 of 4.4536%. Alternatively invest for two years at z2 = 3.4197%. Compute final value for each route and confirm they are equal (rounded). Which pair is correct?
A three-month money market reference rate MRR3m = 1.25% and a six-month MRR6m = 1.75% (annual quoted). Convert the six-month semiannual APR into a quarterly APR equivalent then compute the three-month implied forward IFR3m,3m (annualized). Which is closest?
A forward contract on a stock was set at F0(T) = 100 to be settled in one year. Today the stock price jumps to S0+ = 110 immediately after initiation. With discrete r unchanged, how does this instant change affect the MTM value V0+(T) to the forward buyer?
A forward contract on an asset with no carry has F0(T) = S0(1 + r)^T. At some t>0 with remaining time τ = T - t, the present value of the forward price is F0(T)(1 + r)^{-τ}. Express the long forward MTM V_t(T) in terms of S_t and PV of F0(T).
A commodity forward price is substantially below the no-arbitrage forward computed including storage and financing. Which phenomenon might this indicate?
A forward contract was struck at F0(T) = 200 for T = 1 year. Three months later, with 9 months remaining, the spot has fallen and the current PV of forward is 195.0. From the short seller perspective, is there an MTM gain or loss and what is its magnitude per unit?
Suppose a stock index futures on an exchange for 1 year has f0(T) = [S0 - PV(dividends)](1 + r)^T. Why do exchange-traded futures and OTC forwards with same underlying sometimes have slightly different prices despite same formula?
You observe current spot S0 = 16.909 ZAR/EUR, six-month ZAR rate 3.5%, six-month EUR rate -0.5%. A six-month ZAR/EUR forward is quoted at 17.2506. If spot instantaneously appreciates to 16.50 with other factors unchanged, what is the sign of the MTM from the forward seller's perspective?
Given zero-coupon bond discount factors DF1 = 0.976601 and DF2 = 0.934961, what are the implied zero rates z1 and z2 (annual discrete)?
A trader wants to lock in borrowing costs for a future one-month loan starting in three months. Which instrument is designed for fixing a single future short-term rate for a given period?
A bank has a future liability in three months of USD 1,000,000 that will accrue at the one-month USD MRR. It enters a pay-fixed FRA starting in three months for one month at the FRA rate IFR3m,1m. If the realized MRR at that future time is higher than the FRA rate, what is the FRA buyer's payoff direction at settlement?
Suppose a two-year zero rate z2 = 3.4197% and three-year zero z3 = 4.0005%. What is the implied one-year forward rate starting in two years (IFR2,1)?
In the presence of known storage cost of USD 2 and risk-free rate 2%, spot gold S0 was 1,783.28 to satisfy no-arbitrage for a given forward F0. If storage cost payable at maturity increases sharply, what is the immediate qualitative change to the no-arbitrage forward price?
A forward contract on an underlying with no additional cost was priced at initiation so V0 = 0. If interest rates rise immediately after initiation, holding other parameters constant, what happens to the present value of the forward price and the forward seller's MTM?
You observe a two-year zero-coupon bond price of 92.45 for face 100. If the two-year zero rate is 3.42% annual, what arbitrage exists and how to exploit it (qualitative)?
Given spot S0 = 100, and continuous compounding risk-free rate r = -0.25% (negative), what is the direction of forward price F0(T) relative to S0 for some T>0 (no carry)?
A forward price F0(T) on an equity index is observed to be much higher than S0(1 + r)^T after accounting for dividends. What is the likely arbitrage trade to exploit this (qualitative)?
A forward price was agreed at 102 for T=0.5. If three months later (t=0.25) spot S_t = 100 and r = 5% (annual), what is the MTM value to the long forward (use discrete compounding)?
A forward contract replicating strategy for a long forward can be created by:
A forward on an asset with known dividend yield is priced using discrete PV of dividends. If an expected dividend occurs exactly halfway to maturity and again at maturity, how should you treat these in the forward formula?
If the foreign risk-free rate is greater than the domestic risk-free rate, what is the forward FX relationship for price quoted as units of foreign currency per one unit of domestic currency (S_{f/d})?
A forward contract on a non-dividend-paying stock was initiated at F0(T) = 51.23 with S0=50 and r=5% for T=0.5. If after three months spot St = 50.50, what is the MTM from the buyer's perspective (three months later), using discrete compounding?
A commodity forward is quoted much higher than the spot adjusted for standard carry, and many traders begin borrowing physical commodity to sell forward. What market force will act to remove the arbitrage?
You have S0 = 1,000 of a commodity, PV of storage cost = 2 at t=0, and r = 2% annual. What is the forward price in three months using discrete compounding (T=0.25)?
When computing an FX forward for AUD/USD with spot S0 = 1.3335, rf_AUD = 0.05% (six-month), rd_USD = 0.20% (six-month), what does the forward formula show about which currency trades at forward premium or discount?
A trader observes one-month MRR = 1.20% APR and two-month MRR = 1.50% APR. Approximate the 1m1m forward rate (one-month forward one month hence) by converting rates and solving. Which is closest?
A 6-month forward on a currency is priced using continuous compounding as F0 = S0 e^{(r_f - r_d)T}. If domestic rates drop unexpectedly, what happens to the forward price (domestic currency in denominator) all else equal?
An investor sells a forward and simultaneously buys the underlying by borrowing at r. Which forward position have they replicated and why?
A forward contract is initiated with F0(T) determined by no-arbitrage. Which of the following factors does NOT enter into the no-arbitrage forward formula for an asset with deterministic known dividends and storage costs?
A forward contract on an asset with per-period (discrete) income rate i and per-period cost rate c under continuous compounding has forward price F0(T) = S0 e^{(r + c - i)T}. What sign on (r + c - i) causes F0 to be less than S0?
If a forward contract for delivery in T has F0(T) = S0(1 + r)^T and an investor instead observes forward at lower price, what arbitrage action creates risk-free profit?
Consider Montau AG expecting KRW 650 million in 75 days with spot KRW/EUR = 1300, r_KRW = 0.75%, r_EUR = -0.25% (annual, continuous). Compute the 75-day KRW/EUR forward consistent with no-arbitrage (rounded).
A forward contract on an equity with known quarterly dividends has initial forward price F0(T) that incorporated PV of dividends. If one of those dividend payments is unexpectedly cancelled after trade initiation, what happens to the MTM value of the existing forward position (assuming other parameters unchanged)?
An investor faces a choice: buy a six-month equity forward at F0 = 102, or replicate it by borrowing at r and buying the stock. Under no-arbitrage, which is true?
Consider an underlying with no carry and r = 2% annual discrete. For T=1, if observed forward F0 = S0(1 + r) despite small market frictions, which of the following best describes the relation?
A forward contract on an index with underlying benefits (dividend yield) has forward F0(T) less than S0 if benefits > r + costs. Which variable most directly reduces F0(T) in the discrete formula F0 = [S0 - PV(I) + PV(C)](1 + r)^T?
A 6-month forward on a stock with known dividend schedule is priced at F0. At t = 4 months (two months to maturity) you compute V_t(T) = S_t - PV_t(F0). If a dividend is paid at t = 5 months, how should PV_t(F0) be adjusted relative to t=0 PV?