Topic: FRA Pricing and Value

8. Compute the implied forward rate (fixing rate) of a 1 x 4 FRA. The current 30-day MRR is 4% and the 120-day MRR is 5%. (Use simple interest for FRA.) Fixing rate of FRA is the forward rate of interest from day 30 to day 120. This is quoted in annualized term. Assume 1 month = 30 days unless otherwise informed.

9. A  1 x 4 FRA has 5.316% as fixing rate. At contract maturity or expiration, the 90-day MRR becomes 6%. Notional principal is $10 million. What is the value of along FRA (fixed rate payer) at expiry or what is the cash settlement of the contract at its expiry for a long position?

10. The 30 day and 120 day spot market reference rates are 1% and 2%. What is the price of a 1 x 4 FRA with notional value $1MM? (Price of FRA here refers to the no-arbitrage annualized forward rate of the contract versus 90-day MRR).

Suppose 20 days after trade date of the FRA contract, the 10 day MRR and the 100 day MRR are 1.5% and 3% respectively. If the original FRA buyer wishes to close out the position, how much would he gain at maturity of the FRA? (Note for FRA, use the money market basis or simple interest and day count #days/360 for calculation.)

Topic: Finding Fixed Rate on a Plain-Vanilla Interest Rate Swap

11. A  1-year plain vanilla interest rate  swap has quarterly settlements. Notional principal is $10 million. The annualized MRR spot rates today are: R90-day  = 0.030, R180-day  = 0.035, R270-day  = 0.040, and R360-day  = 0.045. Find the fixed rate (or swap price) in percentage terms. Find the quarterly fixed payments in $.

Topic: Valuing a Plain-Vanilla Interest Rate Swap between payment dates

12.   A 1-year LIBOR plain vanilla interest rate swap with quarterly payments is priced at 6.052% at initiation when 90-day MRR was 5.5%. 30 days later, the annualized MRR rates areas follows: L60-day  = 6.0%, L150-day  = 6.5%, L240-day  = 7.0%, L330-day  = 7.5%. Notional principal is $20 m. Compute the value of the swap to the fixed-rate payer after 30 days.

Topic: Option Pricing

13. An XEO European index put with strike 980 sells for $50. Multiplier for contract is $25 per price point. Index price at expiry of put is 970. What is the net profit or loss of the buyer of the put at expiry?

14. European call and put on an underlying asset with current price $11, are selling at $2.50 and $1 respectively. Both call and put strike prices are the same at $10. What is the current price of a   zero-coupon risk-free bond with $1 parmaturing at the sametime as the expiry of the options?

15. ABC stock price is $9. Use the Black-Scholes model to find the price of ABC stock European put option given that the put has time to expiry or maturity of 6 months. The put strike price is $8. Risk-free interest rate is 3% p.a. Volatility of the ABC stock return is 20% p.a. ABC stock does not issue dividends. (Hint: Black-Scholes European put price is pt  =  Xe−r(T-t) N( – d2) − St  N( – d1) where d1 = [ ln(St/X) + (r+½σ2)(T–t) ] / [ σ√(T–t) ] and d2 = d1 – σ√(T–t). )

16. Viswan Family Office (VFO) wants to buy a 3-month European call option with exercise price INR 320 on a non-dividend paying Biomian stock. The share is trading at INR 300. A 3-month European put with exercise price INR 320 on the same stock is trading at INR 50. Risk-free rate is 4.5%. What should VFO expect to pay for the call option? (Use discrete annual compounding.)

17. HighTech Investment Co. wants to buy XYZ stock. But the XYZ stock market is not liquid and the ask price is too high. However, call options and put options on XYZ stock at exercise price $20 with maturity at 6 months are available at $10 and $2 respectively. Risk-free rate is 5%. What is the price of a synthetic stock that HighTech can purchase? (Use discrete annual compounding.)

18. A European call option on a stock, has an exercise price of $20, and a price premium of $5. A forward  contract  on  the  same  stock  with  the  same  expiry  as  the  call  option  has  an  initial forward price of $20. What is the breakeven price of the underlying stock at maturity for a long call option position? (Ignore the interest opportunity cost of paying the call premium up-front.) What is the equivalent put position to a portfolio of long position in 1 forward contract and short 1 call?

19.  A European call option on Asset K that expires in 6 months has strike price 10 and option price

3. The forward price of Asset K in 6 months is 12. The annual continuously compounded interest rate is 0.04. What is the no-arbitrage equilibrium price of a European put option on Asset K with strike price of 10 and expiry in 6 months?

Topic: Hedging

20. A bank finances its housing loan business by fixed deposits. It pays its depositors  1.5% p.a. on their 3-year SGD fixed deposits. On the other hand, it lends out mortgage loans at floating rate SIBOR + 1% p.a. The bank is concerned if SIBOR may drop in the next 3 years, and decides to hedge by a 3-year interest rate swap. Assume annual interest payments in all the loans and swap structures. If the bank’s counter-party is willing to pay fixed 2% p.a., should the bank buy or sell the swap and what is the floating rate that the bank will pay if it plans to make a net 1%?

21. Watter Investment holds 1 million ABC shares. Watter foresees a possible imminent fall in ABC share price but it needs time to sell the stocks at reasonably good prices. Show how Watter can use short-maturity European options to hedge the possible imminent fall in ABC share price. An ABC put has delta – 0.42 and an ABC call has delta 0.58. Each call or put payoff is based on 1,000 shares. What should the call position be to apply a delta-neutral hedge on the stocks? What should the put position be to  apply  a  delta-neutral hedge  on  the  stocks?  Which  is  a  more reasonable option to use in this case if Watter does not want to expense for the hedge?

22. Trader firm BestCom is betting on ABC shares undergoing imminent large volatility in its return. However, it is not sure if ABC price will imminently rise or fall. ABC put has delta – 0.42 and an ABC call has delta 0.58. Each call or put payoff is based on 1,000 shares. Bestcom is planning to transact in 1 million ABC shares for this betting strategy. What positions should Bestcom hold in the short-run that involve the smallest cash outlay?