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Endpräsentation Diplomarbeit
Analysis and valuation of interest rate swap optionsBetreuer: Prof. Dr. Günther Pöll
Themes Introduction Market for fixed income and interest
rate swaps Basic valuation methods for fixed
income assets Basics of options and swaptions Valuation of interest rate swap
options Conclusion
Introduction The basics of fixed income assets
coupon rate maturity date, issued amount, outstanding amount, issuer, issue date market price, market yield, Contractual features and Credit-rating category
Interest rate Swaps: Exchange of a fixed interest rate with a floating rate
Option on Interest rate Swaps: swaption Swaptions are derivatives of swaps
Market for fixed income and interest swaps Market for fixed income assets
Primary Secondary
Participants Issuers Intermediaries Investors
Key players Governments Central banks Corporations Banks Financial institutions and dealers Households
Market for fixed income and interest swaps
Market for fixed income and interest swaps
Basic valuation methods for fixed income assets Value of continously compounded fixed
deposit:
Zero-Coupon bond countinously compounded:
Yield curve given a set of bond prices
Basic valuation methods for fixed income assets
Forward interest rate:
For Instantenous fr, fr and yield curve are given by:
Basics of options and swaptions Option gives buyer the right (not the obligation to buy (call
option) or sell (put option) an aggreed quantity n of a predetermined underlying S at a specific price, the strike X at maturity T.
3 kind of options: European options American options Bermudan options
3 price points: at-the-money in-the-money out-of-the-money
Basics of options and swaptions Black-Scholes-Merton model Following example for a ۲ by T European payer swaption with fixed coupon
rate c. FSR(0, ۲,T) is the forward swap rate and using A(t, ۲,T) as the numeraire leads to the following solution
Practical usage with following discount factors: D(0,1y) = 0.95, D(0,1.5y) = 0.925, D(0,2y) = 0.9, D(0,2.5y) = 0.875, D(0,3y) = 0.85 and the implied volatility is 18.5%. First step for calculating a ATM forward payer swaption is to calculate the 2-year par swap rate at 1 year foward with semiannual payment:
Basics of options and swaptions Strike K equals the forward swap rate, K = 5,663. The
maturity of the option is 1 year (T0 = 1) and the volatility is σ = 0.185. Plugging in Blacks formula and testing for expected value.
Final price of the swaption:
Valuation of interest rate swap options-factor models Modelling yield curve and term
structure how interest rates of a given maturity
evolve over time All prices develop under the assumption
of no arbitrage Forward rates do not have to be
lognormally distributed like in Black‘s formula
Valuation of interest rate swap options-factor models
The Vasicek model Developement of short term interest rate
r as simple mean reverting process
The Cox-Ingersoll-Ross model Similiar like Vasicek and volatility
depends of the level of r
Valuation of interest rate swap options-factor models
The Heath-Jarrow-Morton model Drift term and white noise process Forward rate is driven by the white noise
process Shock at t from R(t) influences all future
rates
Valuation of interest rate swap options-market models Market models are directly based on
market data Parameters set from historical data
Libor market model Uses Libor rates as input
Swap market model Uses swap rates as input
String market model Interprets every distinct point at the term
structure as random variable
Valuation of interest rate swap options-market models
Conclusion
Massive increase of the volume of interest rate derivatives since 2000
Higher debt levels are the main reason for the volume increase in interest rate derivatives and swaptions
Market models with 3-4 factors are best for describing term structure