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Options, Caps, Floors and Collars Chapter 25 Financial Institutions Management, 3/e By Anthony Saunders Irwin/McGraw-Hill 1 Call Options on Bonds Buy a call Write a call X X Irwin/McGraw-Hill 2 Put Options on Bonds Buy a Put Write a Put X X Irwin/McGraw-Hill 3 Writing versus Buying Options Many smaller FIs constrained to buying rather than writing options. • Economic reasons » Potentially unlimited downside losses. • Regulatory reasons » Risk associated with writing naked options. Irwin/McGraw-Hill 4 Hedging • Payoffs to Bond + Put Bond X Put Net X Irwin/McGraw-Hill 5 Hedging Bonds Weaknesses of Black-Scholes model. • Assumes short-term interest rate constant • Assumes constant variance of returns on underlying asset. • Behavior of bond prices between issuance and maturity » Pull-to-maturity. Irwin/McGraw-Hill 6 Hedging With Bond Options Using Binomial Model • Example: FI purchases zero-coupon bond with 2 years to maturity, at P0 = $80.45. This means YTM = 11.5%. • Assume FI may have to sell at t=1. Current yield on 1-year bonds is 10% and forecast for next year’s 1-year rate is that rates will rise to either 13.82% or 12.18%. • If r1=13.82%, P1= 100/1.1382 = $87.86 • If r1=12.18%, P1= 100/1.1218 = $89.14 Irwin/McGraw-Hill 7 Example (continued) • If the 1-year rates of 13.82% and 12.18% are equally likely, expected 1-year rate = 13% and E(P1) = 100/1.13 = $88.50. • To ensure that the FI receives at least $88.50 at end of 1 year, buy put with X = $88.50. Irwin/McGraw-Hill 8 Value of the Put At t = 1, equally likely outcomes that bond with 1 year to maturity trading at $87.86 or $89.14. • Value of put at t=1: Max[88.5-87.86, 0] = .64 Or, Max[88.5-89.14, 0] = 0. • Value at t=0: P = [.5(.64) + .5(0)]/1.10 = $0.29. Irwin/McGraw-Hill 9 Actual Bond Options Most pure bond options trade over-thecounter. Preferred method of hedging is an option on an interest rate futures contract. Irwin/McGraw-Hill 10 Using Options to Hedge FX Risk • Example: FI is long in 1-month T-bill paying £100 million. FIs liabilities are in dollars. Suppose they hedge with put options, with X=$1.60 /£1. Contract size = £31,250. • FI needs to buy £100,000,000/£31,250 = 3,200 contracts. If cost of put = 0.20 cents per £, then each contract costs $62.50. Total cost = $200,000 = (62.50 × 3,200). Irwin/McGraw-Hill 11 Hedging Credit Risk With Options Credit spread call option • Payoff increases as (default) yield spread on a specified benchmark bond on the borrower increases above some exercise spread S. Digital default option • Pays a stated amount in the event of a loan default. Irwin/McGraw-Hill 12 Hedging Catastrophe Risk Catastrophe (CAT) call spread options to hedge unexpectedly high loss events such as hurricanes, faced by PC insurers. Provides coverage within a bracket of lossratios. Example: Increasing payoff if lossratio between 50% and 80%. No payoff if below 50%. Capped at 80%. Irwin/McGraw-Hill 13 Caps, Floors, Collars • Cap: buy call (or succession of calls) on interest rates. • Floor: buy a put on interest rates. • Collar: Cap + Floor. • Caps, Floors and Collars create exposure to counterparty credit risk since they involve multiple exercise over-the-counter contracts. Irwin/McGraw-Hill 14