Interest Rate Options [Caps / Floors / Collars] Financial Engineering & Risk Management Interest Rate Options [Caps / Floors / Collars] 제일선물주식회사

Agenda • Caps • Floors • Collars [Caps & Floors] • Bond Options

Caps INTEREST RATE OPTIONS Protection against rising Interest rates Interest rate call option - 변동금리 차입자에게 금리상승 위험을 제거 Rising interest rates ⇒ Rising value of the interest rate call option Cap Payoff = Max[(iT - i) F, 0 ] Example 행사금리[i] 6.0% CD 금리[iT] 7.0% 원금[F] 1백만원 만기기간[] 1년 Cap : 분기 정산일에 시장금리가 캡 금리보다 높으면 차액에 해당하는 이자를 지불 Payoff = Max[(7.0% - 6.0%) ×1 ×1,000,000, 0] = 10,000

Floors INTEREST RATE OPTIONS Protection against falling Interest rates Interest rate put option - 변동금리 대출자에게 금리하락 위험을 제거 Falling interest rates ⇒ Rising value of the interest rate put option Floor Payoff = Max[(i - iT) F, 0 ] Example 행사금리[i] 8.0% CD 금리[iT] 6.0% 원금[F] 1백만원 만기기간[] 1년 Floor : 분기 정산일에 시장금리가 플로어 금리보다 낮으면 차액에 해당하는 이자를 지불 Payoff = Max[(8.0% - 6.0%) ×1 ×1,000,000, 0] = 20,000

Collars [Caps & Floors] INTEREST RATE OPTIONS Cap Payoff Max[(iT - i) F, 0 ] / Max[(7.0%-6.5%) ×1 ×1000000, 0] 행사금리 6.5% CD 금리 7.0% 원금 1백만원 만기기간 1년

Collars [Caps & Floors] INTEREST RATE OPTIONS Floor Payoff Max[(i - iT) F, 0 ] / Max[(7.5%-7.0%) ×1 ×1000000, 0] 행사금리 7.5% CD 금리 7.0% 원금 1백만원 만기기간 1년

Collars [Caps & Floors] INTEREST RATE OPTIONS Collar [Cap + Floor] Collar Payoff = Max[(iT - i) F, 0 ] + Max[(i - iT) F, 0 ]]

Collars [Caps & Floors] INTEREST RATE OPTIONS Long interest rate collar[buy cap / sell floor] = Pay-fixed interest rate swap Short interest rate collar[sell cap / buy floor] = Receive-fixed interest rate swap Cap Floor 금리수준 이자율 옵션 국채옵션 금리상승 위험 Buy Cap Buy Put 금리하락 위험 Sell Cap Sell Put Buy Floor Buy Call Sell Floor Sell Call

Bond Options INTEREST RATE OPTIONS Interest rate option and Zero Coupon Bond Option are equivalent[Cap = Put Option Payoff] 행사가격 = 1 / 행사금리 Zero Coupon Bond Option와 Cap의 Payoff를 동일한 유통수익률로 할인 1 1 1 --------- Max[(iT-1 - i, 0] = (1 + i) Max[ ------- - ---------, 0] 1 + iT-1 1 + i 1 + iT-1 Exercise interest rate 5.0% / 1 period before maturity 유통수익률 Zero coupon bond option [Put] Interest rate option [Cap] 7.00% 1.05 Max[1/1.05-1/1.07,0] = 0.01869 Max[0.07-0.05,0] / 1.07 = 0.01869 5.50% 1.05 Max[1/1.05-1/1.055,0] = 0.00474 Max[0.055-0.05,0] / 1.055 = 0.00474 4.00% 1.05 Max[1/1.05-1/1.04,0] = 0.00000 Max[0.07-0.05,0] / 1.04 = 0.00000

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