Konkavitas dolar dan prediksi harga obligasi

Penilaian dan Analisis Obligasi dengan Python

Joshua Mayhew

Options Trader

Konkavitas dolar

Konkavitas = % perubahan durasi untuk perubahan yield 1%
Konkavitas dolar = perubahan $ durasi untuk perubahan yield 1%:

$ \text{Dollar Convexity} = \text{Convexity} \times \text{Bond Price} \times 0.01^2$

Contoh konkavitas dolar

Obligasi 10 tahun, kupon 3%, yield 5%, nilai nominal USD 100. Berapa konkavitas dolarnya?

price = -npf.pv(rate=0.05, nper=10, pmt=3, fv=100)
price_up = -npf.pv(rate=0.06, nper=10, pmt=3, fv=100)
price_down = -npf.pv(rate=0.04, nper=10, pmt=3, fv=100)
convexity = (price_down + price_up - 2 * price) / (price * 0.01 ** 2)
dollar_convexity = convexity * price * 0.01 ** 2
print("Dollar Convexity: ", dollar_convexity)

Dollar Convexity:  0.69

Penyesuaian konkavitas

Konkavitas dapat meningkatkan prediksi harga obligasi
Penyesuaian konkavitas = seberapa besar harga berubah karena konkavitas

$ \text{Convexity Adjustment} = 0.5 \times \text{Dollar Convexity} \times 100^2 \times (\Delta y)^2$

Contoh penyesuaian konkavitas

Obligasi 10 tahun, kupon 3%, yield 5%, nilai nominal USD 100
Berapa penyesuaian konkavitasnya?

price = -npf.pv(rate=0.05, nper=10, pmt=3, fv=100)
price_up = -npf.pv(rate=0.06, nper=10, pmt=3, fv=100)
price_down = -npf.pv(rate=0.04, nper=10, pmt=3, fv=100)
convexity = (price_down + price_up - 2 * price) / (price * 0.01 ** 2)

dollar_convexity = convexity * price * 0.01 ** 2

convexity_adjustment = 0.5 * dollar_convexity * 100 ** 2 * 0.01 ** 2
print("Convexity Adjustment: ", convexity_adjustment)

Convexity Adjustment:  0.35

Menggabungkan durasi dan konkavitas

Prediksi perubahan harga dari durasi saja:

$ \text{Price Change} = -100 \times \text{Dollar Duration} \times \Delta y$

Prediksi perubahan harga dari durasi dan konkavitas:

$ \text{Price Change} = -100 \times \text{Dollar Duration} \times \Delta y \ + \ \text{Convexity Adjustment}$

$ = -100 \times \text{Dollar Duration} \times \Delta y \ + \ 0.5 \times \text{Dollar Convexity} \times 100^2 \times (\Delta y)^2$

Menggabungkan durasi dan konkavitas meningkatkan estimasi harga

Contoh durasi dan konkavitas

Obligasi 10 tahun, kupon 3%, yield 5%, nilai nominal USD 100:

price = -npf.pv(rate=0.05, nper=10, pmt=3, fv=100)
price_up = -npf.pv(rate=0.06, nper=10, pmt=3, fv=100)
price_down = -npf.pv(rate=0.04, nper=10, pmt=3, fv=100)

duration = (price_down - price_up) / (2 * price * 0.01)
dollar_duration = duration * price * 0.01

convexity = (price_down + price_up - 2 * price) / (price * 0.01 ** 2)
dollar_convexity = convexity * price * 0.01
convexity_adjustment = dollar_convexity * 100 ** 2 * 0.01 ** 2

combined_prediction = -100 * dollar_duration * 0.01 + convexity_adjustment
print("Predicted Price Change: ", combined_prediction)

Predicted Price Change:  -6.64

Ayo berlatih!

Penilaian dan Analisis Obligasi dengan Python