endpräsentation diplomarbeit analysis and valuation of interest rate swap options betreuer: prof....
TRANSCRIPT
![Page 1: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/1.jpg)
Endpräsentation Diplomarbeit
Analysis and valuation of interest rate swap optionsBetreuer: Prof. Dr. Günther Pöll
![Page 2: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/2.jpg)
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
![Page 3: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/3.jpg)
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
![Page 4: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/4.jpg)
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
![Page 5: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/5.jpg)
Market for fixed income and interest swaps
![Page 6: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/6.jpg)
Market for fixed income and interest swaps
![Page 7: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/7.jpg)
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
![Page 8: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/8.jpg)
Basic valuation methods for fixed income assets
Forward interest rate:
For Instantenous fr, fr and yield curve are given by:
![Page 9: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/9.jpg)
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
![Page 10: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/10.jpg)
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:
![Page 11: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/11.jpg)
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:
![Page 12: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/12.jpg)
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
![Page 13: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/13.jpg)
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
![Page 14: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/14.jpg)
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
![Page 15: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/15.jpg)
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
![Page 16: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/16.jpg)
Valuation of interest rate swap options-market models
![Page 17: Endpräsentation Diplomarbeit Analysis and valuation of interest rate swap options Betreuer: Prof. Dr. Günther Pöll](https://reader030.vdocuments.us/reader030/viewer/2022032523/56649d925503460f94a791f0/html5/thumbnails/17.jpg)
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