5.29 get_cms_rate_hagan

Function File: forward_rate= get_cms_rate_hagan(valuation_date, value_type, swap, curve, sigma, payment_date)

Compute the cms rate of an underlying swap floating leg incl. convexity adjustment. The implementation of cms convexity adjustment is based on P.S. Hagan, Convexity Conundrums, 2003. There is a minor issue with Hagans formulas: An adjustment to the value of the swaplet / caplet / floorlet is being calculated. For calculation of this adjustment a volatility is required. The volatility has to be interpolated from a given volatility cube with a given moneyness. In case of swaplets, the moneyness can be assumed to be 1.0. For caplets / floorlets, the moneyness can be calculated as (cms_rate-X) or (cms_rate/X). Here either the adjusted cms rate or still the unadjusted cms rate can be used to calculate the moneyness.
Explanation of Input Parameters:

• valuation_date: valuation date
• value_type: value type (e.g. base or stress)
• swap: swap instrument object, underlying of cms swap
• curve: discount curve object
• sigma: volatility used for calculating convexity adjustment
• payment_date: payment date of cashflow

See also: discount_factor, timefactor, rollout_structured_cashflows.