Everything You Always Wanted to Know about Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask

Abstract. We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.

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“…By relying on bootstrapping techniques (see e.g. [1]), the following curves can be obtained from OIS rates:…”

Section: Modeling the Post-crisis Interest Rate Marketmentioning

confidence: 99%

A general HJM framework for multiple yield curve modelling

2016

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“…Under well-known assumptions the valuation of a future cash flow can be written as an expectation, 2 that is the time t 0 -value V (t 0 ) is…”

Section: Foundations Assumptions Notationmentioning

confidence: 99%

“…That is, we could define t → N(t) and t → I(t) to be F t 0 -measurable for all times t and still generate any given discount curve and forward curve, respectively. There 2 Since we are only considering the linearity of the valuation at a fixed time t 0 , we just require that some fundamental theorem of asset pricing holds, for example, assuming that the price processes are locally bounded semi-martingales and the no free lunch with vanishing risk condition holds, [7]. 3 We will use the notation P(T ; t) (instead of the more common P(t, T )) for a the time-t value of zero-coupon bond maturing in T , since we consider t = t 0 as fixed.…”

Section: Definition 1 Let I Denote An Index That Is I(t )mentioning

confidence: 99%

“…A very detailed description of multi-curve bootstrapping, which also details market conventions and convexity adjustments of the calibration instruments, can be found in [2]. For market conventions also see [17].…”

Section: Definition 1 Let I Denote An Index That Is I(t )mentioning

confidence: 99%

“…If a curve interpolation should also be used for times t > t 0 within a dynamic multi-curve model, then this may impose additional constraints on the admissible interpolations schemes. For example, (2) implies that linear interpolation of time-t zero-coupon bond prices for t > t 0 implies linear interpolation of the time-t zero-coupon bond prices, which in turn implies a special interpolation of forward rates in a LIBOR market model, see Sect. 19.5 in [10].…”

Section: Definition 1 Let I Denote An Index That Is I(t )mentioning

confidence: 99%

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Multi-curve Construction

Fries

2016

Innovations in Derivatives Markets

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In this chapter we discuss the definition, construction, interpolation and application of curves. We will discuss discount curves, a tool for the valuation of deterministic cash-flows and forward curves, a tool for the valuation of linear cashflows of an index. A curve is mainly a tool to interpolate certain basic financial products (zero coupon bonds, FRAs) with respect to maturity date and fixing date, such that it can be used to value products, which can be represented as linear functions of possibly interpolated values of a discount or forward curve. For this, the chosen interpolation method and interpolation entity plays an important role. Distinguishing forward curves from discount curves (representing the collateralization of the forward) motivates an alternative interpolation method, namely interpolation of the forward value (the product of the forward and the discount factor). In addition, treating forward curves as native curves (instead of representing them by pseudodiscount curves) will avoid other problems, like that of overlapping instruments. Besides the interpolation, we discuss the calibration of the curves for which we give a generic object-oriented implementation in Fries (Curve calibration. Object-oriented reference implementation, 2010-2015, [11]). We give some numerical results, which have been obtained using this implementation and conclude with a remark on how to define term-structure models (analog to a LIBOR market model) based on the definition of the performance index of an accrual account associated with a discount curve.

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Discounting and Derivative Pricing Before and After the Financial Crisis: An Introduction

Veronesi

2016

Handbook of Fixed‐Income Securities

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Everything You Always Wanted to Know about Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask

Cited by 42 publications

References 29 publications

A general HJM framework for multiple yield curve modelling

A general HJM framework for multiple yield curve modelling

Multi-curve Construction

Discounting and Derivative Pricing Before and After the Financial Crisis: An Introduction

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