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\title{Derivatives Lab}
\author{Session 4}
\date{September 13, 2011}
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\begin{enumerate}

\item Consider a 10-year level coupon bond with an annual coupon rate
of 8\% compounded annually and a par value of EUR 1\,000.  Plot the
price of the bond vs.\ the yield.

\item Plot price volatility vs.\ time to maturity for level coupon
bonds with annual coupon rates of 2\%, 6\%, and 12\% paid semiannually.
Assume a yield of 6\% and a par value of EUR 1\,000.  To see the
different volatility behaviors, take a range from 0 up to 100 years to
maturity. 

\item Plot the bond value (forward value) of an 8\% 15-year bond
compounded semi-annually vs.\ years to maturity under three rate
scenarios: (a) the interest rate decreases instantaneously to 6\%, (b)
the interest rate remains unchanged, and (c) the interest rate
increases instantaneously to 10\%.

\item Plot the future value of a 30-year bond at a coupon rate of 10\%
compounded annually after a 10-year horizon as a function of yield.
Find the minimum of the horizon price numerically, e.g., using
\texttt{scipy.optimize.brent}. 

\item Write out a consistent set of expressions for the Macaulay
duration and the immunization of a level coupon bond assuming
continuous compounding of interest.

\end{enumerate}


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