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On cash settled IRR-swaptions and Markov functional modeling

Bermin, Hans-Peter LU and Williams, Gareth (2017) In International Journal of Theoretical and Applied Finance 20(2).
Abstract
In this paper, we show how to consistently price cash settled Internal Rate of Return (IRR)-swaptions and derivatives on these contracts. There are several results worth highlighting. First, if we know at what fixed coupon an IRR-swap values to par, we can compute the price of any IRR-swaption in a way consistent with absence of arbitrage. We show that this fixed coupon, denoted the IRR-forward, carries an additional convexity adjustment. The size of the adjustment depends mainly on the shape of the volatility surface but also on the skew of the forward. The largest convexity adjustments are seen for IRR-forwards referencing long tenors and long expiries. Second, we show that any Markov functional technique, relating a given term-structure... (More)
In this paper, we show how to consistently price cash settled Internal Rate of Return (IRR)-swaptions and derivatives on these contracts. There are several results worth highlighting. First, if we know at what fixed coupon an IRR-swap values to par, we can compute the price of any IRR-swaption in a way consistent with absence of arbitrage. We show that this fixed coupon, denoted the IRR-forward, carries an additional convexity adjustment. The size of the adjustment depends mainly on the shape of the volatility surface but also on the skew of the forward. The largest convexity adjustments are seen for IRR-forwards referencing long tenors and long expiries. Second, we show that any Markov functional technique, relating a given term-structure model to the market observed IRR-swaptions, should be carried out with respect to the corresponding forward measure. The modification of the forward swap rate is further shown to consistently value the fixed and the floating leg of the underlying IRR-swap correctly. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
swaptions, IRR, convexity, term structure, linear Gaussian model, quadratic Gaussian model, Markov functional
in
International Journal of Theoretical and Applied Finance
volume
20
issue
2
pages
20 pages
publisher
World Scientific
external identifiers
  • scopus:85015440016
  • wos:000398041100002
ISSN
0219-0249
DOI
10.1142/S0219024917500091
language
English
LU publication?
yes
id
d5388306-7937-4a73-9a82-56e37f506727
date added to LUP
2017-02-27 11:39:21
date last changed
2018-01-07 11:52:52
@article{d5388306-7937-4a73-9a82-56e37f506727,
  abstract     = {In this paper, we show how to consistently price cash settled Internal Rate of Return (IRR)-swaptions and derivatives on these contracts. There are several results worth highlighting. First, if we know at what fixed coupon an IRR-swap values to par, we can compute the price of any IRR-swaption in a way consistent with absence of arbitrage. We show that this fixed coupon, denoted the IRR-forward, carries an additional convexity adjustment. The size of the adjustment depends mainly on the shape of the volatility surface but also on the skew of the forward. The largest convexity adjustments are seen for IRR-forwards referencing long tenors and long expiries. Second, we show that any Markov functional technique, relating a given term-structure model to the market observed IRR-swaptions, should be carried out with respect to the corresponding forward measure. The modification of the forward swap rate is further shown to consistently value the fixed and the floating leg of the underlying IRR-swap correctly.},
  articleno    = {1750009},
  author       = {Bermin, Hans-Peter and Williams, Gareth},
  issn         = {0219-0249},
  keyword      = {swaptions,IRR,convexity,term structure,linear Gaussian model,quadratic Gaussian model,Markov functional},
  language     = {eng},
  month        = {02},
  number       = {2},
  pages        = {20},
  publisher    = {World Scientific},
  series       = {International Journal of Theoretical and Applied Finance},
  title        = {On cash settled IRR-swaptions and Markov functional modeling},
  url          = {http://dx.doi.org/10.1142/S0219024917500091},
  volume       = {20},
  year         = {2017},
}