Consider two two$-$year, $7\%$ annual coupon bonds. Two bonds are same except that one is callable in one year at $$100$ and the other is putable in one year at $$100.$ Value the embedded call and put option for each bond per $$100$ of par value.

Par yield for maturity $1$ year and $2$ years are $4\mathrm{.}5749000\%$ and $5\mathrm{.}3844204\%$ respec$-$ tively. The volatility of interest rates is assumed to be $15\%.$