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# Calculating a European Call Option

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Attached is a problem which requires the calculation of a European Call Option. I would appreciate your assistance in solving this problem so I can use the solution as model to help me understand all the concepts behind writing European Call Options as I am preparing to do the homework.

I searched for the solution in the Library but couldn't locate anything similar to the way this problem is laid out.

Mini - Case Study

Melissa Sanders, a recent MBA graduate in finance and accounting from Regis University, is an analyst at a local hedge fund. The fund wishes to sell (write) European calls on 2-year, 4.5% coupon Treasury notes. The notes currently sell for \$98.90. The one-year forward rate (r0) is 4.65 percent. The assumed one-year forward rate one year from now (r1,L) is 5.0 percent. The standard deviation is 10 percent. Fill in the seven boxes of the following binomial tree. ASSUME EACH STATE HAS A PROBABILITY OF 50% AND INTEREST IS PAID ANNUALLY. Show your work.

#### Solution Preview

Here, r1,L = 5%, and s = 0.10
The standard exponential function is e2s = EXP(2s)
Then r1,H = r1,L(e2s) = r1,L* EXP(2s)
= 0.05*EXP(2 x 0.10)
= 0.0375(1.2214)
= 0.0611 or 6.11%.

Note: the expected interest rate one year from now according to the binomial tree is:
6.11%*(0.5) + 5%*(0.5) = 5.56%

The two-year Treasury notes, will unambiguously pay 100 percent of par ...

#### Solution Summary

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\$2.49