# Irwin/McGraw-Hill 1 Options, Caps, Floors and Collars Chapter 25 Financial Institutions Management, 3/e By Anthony Saunders.

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Irwin/McGraw-Hill 1 Options, Caps, Floors and Collars Chapter 25 Financial Institutions Management, 3/e By Anthony Saunders

Irwin/McGraw-Hill 2 Call Options on Bonds Buy a callWrite a call X X

Irwin/McGraw-Hill 3 Put Options on Bonds Buy a PutWrite a Put X X

Irwin/McGraw-Hill 4 Writing versus Buying Options n 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 5 Hedging Payoffs to Bond + Put X X Put Bond Net

Irwin/McGraw-Hill 6 Hedging Bonds n 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 7 Hedging With Bond Options Using Binomial Model Example: FI purchases zero-coupon bond with 2 years to maturity, at P 0 = \$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 r 1 =13.82%, P 1 = 100/1.1382 = \$87.86 If r 1 =12.18%, P 1 = 100/1.1218 = \$89.14

Irwin/McGraw-Hill 8 Example (continued) If the 1-year rates of 13.82% and 12.18% are equally likely, expected 1-year rate = 13% and E(P 1 ) = 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 9 Value of the Put n 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 10 Actual Bond Options n Most pure bond options trade over-the- counter. n Preferred method of hedging is an option on an interest rate futures contract.

Irwin/McGraw-Hill 11 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 12 Hedging Credit Risk With Options n Credit spread call option Payoff increases as (default) yield spread on a specified benchmark bond on the borrower increases above some exercise spread S. n Digital default option Pays a stated amount in the event of a loan default.

Irwin/McGraw-Hill 13 Hedging Catastrophe Risk n Catastrophe (CAT) call spread options to hedge unexpectedly high loss events such as hurricanes, faced by PC insurers. n Provides coverage within a bracket of loss- ratios. Example: Increasing payoff if loss- ratio between 50% and 80%. No payoff if below 50%. Capped at 80%.

Irwin/McGraw-Hill 14 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.

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