Abstract
After examining the implications of our theoretical term structure model on the different term structures that are relevant in pricing term structure derivatives we now answer the question on how the model can be used in risk management. The management of interest rate risk is especially concerned with rebalancing a fixed income portfolio exposed to interest rate risk due to the desired risk return characteristics. The types of interest rate risk considered to be of relevance in interest rate risk management are generally considered to be: (i) Market risk is the risk of changing prices due to general changes of the overall level of interest rates on default free securities, (ii) yield curve risk is considered the risk associated with non-parallel shifts in the yield curve, i.e. a reshaping of the yield curve due to, for example, steepening, flattening, or twisting, and (iii) credit risk which is related to altering security prices caused by changes in the creditworthiness of the issuer.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
See, for example, Macaulay (1938) and Bierwag, Kaufman, and Toevs (1983).
Other recent concepts include the functional duration from Klaffky, Ma, and Nozari (1992) and the partial duration by Waldman (1992).
For a comparative analysis of current credit risk models used as internal models by banks see, for example, Crouhy, Galai, and Mark (2000).
See, for example, Wu (1996) and Chen (1996a).
For a broad variety of applications of this method see, for example, Musiela and Rutkowski (1997).
A method studied extensively for different contingent claims by, for example, Wilmott, Dewynne, and Howison (1993).
For the complete definitions and the relevant conditions see, for example, Duffle (1996), Karatzas and Shreve (1991), and Oksendal (1995).
For example, the previously derived discount bond formula is the solution to
This results in discounted asset prices being martingales with respect to ℚ; see Harrison and Pliska (1981) and Geman, Karoui, and Rochet (1995).
From now onwards we drop the notation for the x-dependence of discount bonds, i.e. we denote their price by P (t, T).
The technique of changing numéraire was developed by Geman (1989) for the general case of stochastic interest rates. Jamshidian (1989) implicitly uses this technique in the Gaussian interest rate framework of Vasicek (1977).
See, for example, Dothan (1990, p. 288).
See, for example, Oksendal (1995).
The put-call parity was first described by Stoll (1969).
For the origin and the development of the swap markets see, for example, Das (1994, ch. 1).
For variant forms of interest rate swaps see, for example, Marshall and Kapner (1993, ch. 3).
For the pricing of default-free interest rate caps, for example, under the direct approach see Briys, Crouhy, and Schöbel (1991) and under the log-normal approach see Miltersen, Sandmann, and Sondermann (1997).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kellerhals, B.P. (2001). Risk Management and Derivatives Pricing. In: Financial Pricing Models in Continuous Time and Kalman Filtering. Lecture Notes in Economics and Mathematical Systems, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21901-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-662-21901-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42364-5
Online ISBN: 978-3-662-21901-0
eBook Packages: Springer Book Archive