Variable rate swap is an interest rate swap that has two legs: one fixed rate leg and a variable rate leg. The variable leg involves fixed rate payments for an initial period of time and a floating rate for the rest. The floating rate on that portion is defined as a minimum of two index rates

Tim Xiao

Humanities Commons

Variable Rate Swap Model  Variable rate swap is an interest rate swap that has two legs: one fixed rate leg and a variable rate leg. The variable leg involves fixed rate payments for an initial period of time and a floating rate for the rest. The floating rate on that portion is defined as a minimum of two index rates.  The fixed rate leg is similar to a fixed rate bond. The bond price is computed by discounting each coupon descripted at https://finpricing.com/lib/FiBond.html  We treat the two index rates as assets whose values are lognormally distributed random variable. Their pricing procedure uses discount factors retrieved from the EURIBOR curve.  The present value of the minimum of two assets, s1 and s2, is given by the formula  p D T s Ns ss Ns s=−+−( )[ (ln( / ) /) (ln( / ) /)]12 1221 222 2  (1)  where  •     2 12221 22= + −( )T , • 1 and 2 are the volatilities of s1 and s2 respectively, •  is the correlation of the two risk factors, • T is the maturity time, • s1  and s2 are the expected values of s1 and s2 at maturity (future values), • D(T) is the discount factor implied by the yield curve.  It is forward two index rates as retrieved from the yield curves that should be used for s1  and s2 . The minimum of two values, s1 and s2, can be expressed as   p = min(s1,s2) = s1 – max(s1-s2, 0)    (2)  If s1 and s2 are two risky assets, the present value of p at some future time T is   PV p P T E pT( ) ( , ) ( )= 0      (3)  where P(0,T) is the discount factor implied by the yield curve. Assuming the asset values lognormally distributed, the expectation of max(s1-s2, 0) at maturity can be found as the value of the so called “Exchange-One-Asset-for-Another” European option [2,3] and is given by the following equation:   v s Ns ss Ns s=+−−11 2221 222 2(ln( / ) /) (ln( / ) /)   (4)  where  •     2 12221 22= + −( )T  • 1 and 2 are the volatilities of s1 and s2 respectively, •  is the correlation of the two risk factors • T is the maturity time • s1  and s2 are the expected values of s1 and s2 at maturity (future values).  Combined, Eqs. (2), (3) and (4) yield   p P T s Ns ss Ns s=−+−( , )[ (ln( / ) /) (ln( / ) /)]02 212 1221 22  (5)   

Variable Rate Swap Model

https://hcommons.org/deposits/download/hc:47738/CONTENT/variableswap.pdf/

Variable Rate Swap Model

Abstract

Similar works

Full text

Available Versions

Humanities Commons