Financial theory Financial Market

Derivatives - Options

Question: 3

Price today is $95.0 for a 10-year standard bond futures contract

Settlement time: 6 months' time

Call Option same as bond futures contract

Call Option: Expiry date in 6 months

Option Premium: 0.54%

i) Assume interest rates move down 1% between 'today' and the date of expiry/exercise/settlement: What would be the 'payoff' for a futures buying position if rates move down by 1% p.a. between 'today' and settlement?

Bond has an inverse relationship with Interest Rates. If interest rates tend to move down by 1% p.a and as the settlement payment is within 6 months the interest rate that will impact on the prices would be would be 0.5%. The price will increase with $95.475 (Baz J., & Chacko G., 2004).

The payoff for the futures buying position if rate move down by 1% p.a between today and settlement would be:

$ 95.475 - $ 95.0 = 0.475

(ii) Draw the payoff diagram for the relevant option that you could use as an alternative to the futures position

Payoff Diagram on a Call Option

Current Stock Price =

$ 95.00

Strike Price of Option =

$ 95.47

Price of the Option =

$ 0.54

Stock Price

Gross Payoff

Net Payoff

$ 80.47 $ - $ (0.54)

$ 85.47 $ - $ (0.54)

$ 90.47 $ - $ (0.54)

$ 95.47 $ - $ (0.54)

$ 100.47 $ 5.00 $ 4.46 $ 105.47 $ 10.00 $ 9.46 $ 110.47 $ 15.00 $ 14.46 $ 115.47 $ 20.00 $ 19.46 $ 120.47 $ 25.00 $ 24.46

Yellow line showing the net payoff the buyer.

(i) What would be the payoff in

i. If rates move up 1% p.a. between 'today' and settlement?

Bond has an inverse relationship with Interest Rates. If interest rates tend to move up by 1% p.a and as the settlement payment is within 6 months the interest rate that will impact on the prices would be would be 0.5%. The price will decrease with $ 94.525 (Belghitar Y., Clark E., & Judge A., 2008). The payoff for the futures buying position if rate move down by 1% p.a between today and settlement would be:

$ 95.00 - $ 0.475 = $ 94.525

(ii) Draw the payoff diagram for your

(a)(ii) Option if rates instead move up 1% p.a. between 'today' and settlement/exercise date?

Payoff Diagram on a Call Option

Current Stock Price =

$ 95.00

Strike Price of Option =

$ 94.53

Price of the Option =

$ 0.54

Stock Price

Gross Payoff

Net Payoff

$ 79.53 $ - $ (0.54)

$ 84.53 $ - $ (0.54)

$ 89.53 $ - $ (0.54)

$ 94.53 $ - $ (0.54)

$ 99.53 $ 5.00 $ 4.46 $ 104.53 $ 10.00 $ 9.46 $ 109.53 $ 15.00 $ 14.46 $ 114.53 $ 20.00 $ 19.46 $ 119.53 $ 25.00 $ 24.46

(c) Use your above answers to compare the main advantage and disadvantage of using futures VS options

Looking at the above answers; the following has been observed while comparing the main advantage and disadvantage of using futures VS options ...