Effective Markovian Projection: Application to CMS Spread Options and Mid-Curve Swaptions

44 Pages Posted: 29 Mar 2021

See all articles by Mike Felpel

Mike Felpel

University of Wuppertal

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); acadia

Thomas McWalter

University of Cape Town (UCT); University of Johannesburg

Date Written: March 3, 2021

Abstract

Pricing of interest rate derivatives, such as CMS spread or mid-curve options, depends on modelling the underlying single rates. For flexibility and realism, these rates are often described in the framework of stochastic volatility models. In this paper, we allow rates to be modelled within a class of general stochastic volatility models, which includes SABR, ZABR, free SABR and Heston models. We provide a versatile technique called Effective Markovian Projection, which allows a tractable model to be found that mimics the distribution of the more complex models used to price multi-rate derivatives. Three different numerical approaches are outlined and applied to relevant examples from practice. Finally, a new method that involves moment-matching of Johnson distributions is applied to facilitate closed-form pricing formulas.

Keywords: Stochastic volatility, SABR, ZABR, Markovian Projection, Effective PDE, Approximation formula

Suggested Citation

Felpel, Mike and Kienitz, Joerg and McWalter, Thomas, Effective Markovian Projection: Application to CMS Spread Options and Mid-Curve Swaptions (March 3, 2021). Available at SSRN: https://ssrn.com/abstract=3797245 or http://dx.doi.org/10.2139/ssrn.3797245

Mike Felpel

University of Wuppertal ( email )

Gaußstraße 20
42097 Wuppertal
Germany

Joerg Kienitz (Contact Author)

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

acadia ( email )

93 Longwater Circle
Boston, MA 02061
United States

Thomas McWalter

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

University of Johannesburg ( email )

PO Box 524
Auckland Park
Johannesburg, Gauteng 2006
South Africa

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