Question

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Today is 15 June 2020. A forward contract maturing on 10 January 2021 is written on a bond paying coupon rate 3.00% maturing on 19 October 2030, with current price 99.12. The bond pays semi-annual coupons. The OIS curve is flat at 3.10% (with continuous compounding). What is an appropriate price for the forward contract?

		102.20
		99.11
		99.38
		99.18

Answer 1

Spot Price (S) = 99.12

Par Value = $100

Coupon rate = 3%(semi annual)

Forward Maturity date = 10th January 2021

Bond Maturity date = 19th October 2030

OIS rate or risk free rate = 3.1%

From the Bond Maturity date we can say the bond makes coupon payments on 19th April & 19th October every year

There would be 1 coupon /interest payment made before Forward maturity date

We need to discount that interest payment to get the present value of the interest payment today.(15th June 2020)

Time to next coupon payment i.e. from 15th June 2020 to 19th October 2020 = 15(June) + 31(July) + 31(August) + 30(September) + 19(October) = 126 days

Present value of Interest payment = ((coupon rate / 2) * Par value) * e^{- risk free rate * time to next coupon payment / 365}

Present value of Interest payment = ((3% / 2) * 100) * e ^{- 3.1% * (126 /365)}

Present value of Interest payment = 1.484

Time to forward expiry i.e. from 15th June 2020 to 10th January 2021 = 15(June) + 31(July) + 31(August) + 30(September) + 31(October) + 30(November) + 31(December) + 10(January) = 209 days

Value of Forward contract = (Spot price - Present value of Interest payment) * e ^{risk free rate * (time to forward expiry / 365)}

Value of Forward contract = (99.12 - 1.484) * e ^{3.1% * (209 / 365)}

Value of Forward contract = 99.38