compounding = Simple, Continuous, Annual, Semiannual, EveryFourthMonth, Quarterly, Bimonthly, Monthly, SimpleThenAnnual, SimpleThenSemiannual, SimpleThenEveryFourthMonth, SimpleThenQuarterly, SimpleThenBimonthly, or SimpleThenMonthly -- This option specifies the compounding type for the given interest rate.

daycounter = a name representing a supported day counter (e.g. ISDA, Simple) or a day counter data structure created using the DayCounter constructor -- This option provides a day counter which will be used to convert the period between two dates as a fraction of the year.

evaluationdate =  a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies the evaluation date. By default this is set to the global evaluation date (see EvaluationDate).

The Convexity command calculates the convexity of a set of cash flows or a bond.

For a set of cash flows $C_i\left(t\right)$ the convexity is defined as

where $P_t$ is the discount factor at time $t$ implied by the given interest rate.

A bond's convexity is defined as the weighted second derivative of the price function with respect to the interest rate:

The parameter cashflows is a cash flow or a list of cash flows (see FixedRateCoupon, InArrearIndexedCoupon, ParCoupon, SimpleCashFlow, or UpFrontIndexedCoupon).

The parameter bond must be a fixed- or floating-rate bond data structure (see FixedCouponBond, FloatingRateBond, ZeroCouponBond).

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{SetEvaluationDate}\left(''Jan-01-2005''\right)\:$

$\mathrm{paymentdate}≔''Jan-02-2007''$

$\mathrm{paymentdate}≔''Jan-02-2007''$

$\mathrm{cashflow1}≔\mathrm{SimpleCashFlow}\left(100\,\mathrm{paymentdate}\right)$

$\mathrm{cashflow1}≔\mathrm{100.\; on\; January\; 2,\; 2007}$

$\mathrm{Convexity}\left(\mathrm{cashflow1}\,0.03\,\mathrm{evaluationdate}=''Jan-01-2005''\right)$

$4.010966410$

$\mathrm{Convexity}\left(\mathrm{cashflow1}\,0.03\,\mathrm{evaluationdate}=''Jan-01-2004''\right)$

$9.016445862$

$\mathrm{nominalamt}≔100$

$\mathrm{nominalamt}≔100$

$\mathrm{rate}≔0.05$

$\mathrm{rate}≔0.05$

$\mathrm{paymentdate}≔''Jan-01-2015''$

$\mathrm{paymentdate}≔''Jan-01-2015''$

$\mathrm{startdate}≔''Jan-01-2006''$

$\mathrm{startdate}≔''Jan-01-2006''$

$\mathrm{enddate}≔''Jan-01-2010''$

$\mathrm{enddate}≔''Jan-01-2010''$

$\mathrm{coupon}≔\mathrm{FixedRateCoupon}\left(\mathrm{nominalamt}\,\mathrm{rate}\,\mathrm{startdate}\,\mathrm{enddate}\,\mathrm{paymentdate}\right)$

$\mathrm{coupon}≔\mathrm{20.\; on\; January\; 1,\; 2015}$

$\mathrm{Convexity}\left(\mathrm{coupon}\,0.03\,\mathrm{evaluationdate}=''Jan-01-2005''\right)$

$100.$

$\mathrm{bond}≔\mathrm{FixedCouponBond}\left(100\,5\,\mathrm{Years}\,0.05\right)$

$\mathrm{bond}≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$\mathrm{cflows}≔\mathrm{CashFlows}\left(\mathrm{bond}\right)$

$\mathrm{cflows}≔\left[\mathrm{5.\; on\; \text{'}January\; 1,\; 2006\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2007\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2008\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2009\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2010\text{'}}\,\mathrm{100.\; on\; \text{'}January\; 1,\; 2010\text{'}}\right]$

$\mathrm{Convexity}\left(\mathrm{bond}\,0.03\,\mathrm{evaluationdate}=''Jan-05-2000''\right)$

$92.45245571$

$\mathrm{Convexity}\left(\mathrm{cflows}\,0.03\,\mathrm{evaluationdate}=''Jan-05-2000''\right)$

$92.45245571$

The Finance[Convexity] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.