Consider an eight-month Europe

Consider an eight-month European put option on a Treasury bond that currently has 14.25 years to maturity. The bond principal is $1,000. The current cash bond price is $910, the exercise price is $900, and the volatility of the forward bond price is 10% per annum. A coupon of $35 will be paid by the bond in three months. The risk-free interest rate is 8% for all maturities up to one year. Use Black’s model to determine the price of the option. Consider both the case where the strike price corresponds to the cash price of the bond and the case where it corresponds to the quoted price.

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