# chap25 - One can no more ban derivatives than the Luddites...

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Saunders & Cornett, Financial Institut 1 “One can no more ban derivatives than the Luddites could ban power looms in the early nineteenth century.” R. Bliss

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Saunders & Cornett, Financial Institut 2 Financial Options The right, not the obligation, to buy (for a call) or to sell (for a put) some underlying financial security, at a predetermined price (exercise or strike price) at or before a preset expiration date. Hedge by buying (not selling) options. Short hedge: buy puts. Long hedge: buy calls. Can reduce the cost of options hedge using compound options such as caps, collars & floors.
Saunders & Cornett, Financial Institut 3 Pricing Default-free Bond Options Using the Binomial Model Spot Rates: 1 yr 0 R 1 = 5% 2 yr 0 R 2 = 6.5% p.a. Expectations hypothesis implied forward rate 1 R 1 = 8% p.a. Suppose that there is a 50-50 chance that 1 yr rates 1 yr from now will be either 7% or 9% p.a. Bond Valuation using the Binomial Model: Time period 0 Time period 1 Time period 2 ----50%----100/1.09=\$91.74----25%----\$100 \$88.17=100/1.065 2 ----25%----\$100 ----50%----100/1.07=\$93.46-----25%---\$100 ----25%----\$100

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Saunders & Cornett, Financial Institut 4 Pricing a Call Option on the Bond Using the Binomial Model Exercise Price = \$92.60 = .5(91.74) + .5(93.46) Time period 0 Time period 1 Time period 2 ----50%----------------0--------------25%----\$7.40 \$6.93= .5(0)+.5(.86)/1.05 ------25%----\$7.40 +7.40/(1.065) 2 ----50%---\$0.86= \$93.46-92.60-----25%---\$7.40 ----25%----\$7.40= max (0,100-92.60)
Saunders & Cornett, Financial Institut 5 Delta Hedging 2200 δ = P O / P S If the option’s underlying instrument is a bond then δ = P O / B Delta of call >0 Delta of put <0 Out of the money δ is between 0 - 0.5 At the money δ is around 0.5 In the money δ is between 0.5 - 1

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Saunders & Cornett, Financial Institut 6 Example of Delta Neutral Option Microhedge FI intends to sell its T-bond portfolio in 60 days to underwrite an \$11.168m investment project. The T-bonds are 15 yr 8% p.a. coupon with FV=\$10m and yield of 6.75% p.a. T-bond MV = \$11.168m. Step 1: Analyze the risk of cash position. Calculate duration = 9.33 yrs. Risk that price (interest rates) will decline (increase) over the next 60 days. Assume a 50 bp unanticipated increase in T-bond spot interest rates: E
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