Markov-functional interest rate models pdf

Markov functional models are a very powerful class of market models which calibrate and compute prices and greeks quickly. Dynamics and calibration with stochastic volatility parameterisation and calibration of interest rate dynamics new interest rate models with stochastic volatility. Implications for hedging of the choice of driving process. Mar 14, 2007 mathematical finance is the first book to harmonize the theory, modeling, and implementation of todays most prevalent pricing models under one convenient cover.

The hybrid markov functional model extends the singlecurrency interest rate markov functional model to a consistent model of the joint evolution of interest rates and another stochastic underlying. This dissertation explains, in detail, how markovfunctional models work as well as discussing all of the specific models developed in the literature. The defining characteristic of mf models is that pure discount bond prices are assumed at any time to be a function of some lowdimensional process which is markovian in some martingale measure. Sophisticated statistical modelling of derivatives enables practitioners in the banking industry to reduce financial risk and ultimately increase profits made from these transactions. Numerical methods for markov functional models and their stability markov functional models stable numerical schemes theory of interest rate term structure. The main idea of markov functional modeling is the asset to model is a function of an underlying low dimensional markov process x. The class of markov functional models mfm was introduced by hunt, kennedy and pelsser in 15. The assumptions we make here are motivated by two key issues. Pirjol, nonanalytic behaviour in a lognormal markov. Incorporating a volatility smile into the markovfunctional model. Consequently, the intuition behind the familiar sde formulation of the libor market model may be applied to the libor markov.

This dissertation explains, in detail, how markov functional models work as well as discussing all of the specific models developed in the literature. Second, we show that any markov functional technique, relating a given termstructure model to the market observed irrswaptions, should be carried out with. As the second underlying we consider the fx rate but this could also be an equity process. Consider an interest rate swap first resetting in t 0 and paying at t 1,t m, with fixed rate k 0 and year fractions. The libor markov functional model is an efficient arbitragefree pricing model suitable for callable interest rate derivatives. Moreover, we show that the impact of smile can be much larger than the impact of. Phil hunt, joanne kennedy, antoon pelsser markovfunctional interest rate models. Markov functional interest rate models with stochastic. Bermudan swaptions in the markovfunctional libor model. By specifying these models in markovfunctional form, we obtain a. At the abstract level this class includes all current models of practical importance. Model description the presentation of the theoretical background is mainly following 2. Pelsser 2000 markovfunctional interest rate models, finance and stochastics 4 4, 391408.

Markov functional model is appropriately calibrated to \terminal correlations of swap rates that are relevant to the bermudan swaption then the hedging performance of both the multifactor and single factor models are comparable. In a single currency economy a markov functional model can be described as follows. By specifying these models in markovfunctional form, we obtain a specification which is efficient to. Markov functional interest rate models with stochastic volatility.

We then discuss some additional issues arising from the use of markov modeling which must be considered. Markovfunctional models are a very powerful class of market models which calibrate and compute prices and greeks quickly. Pirjol, phase transition in a lognormal markov functional model j. This paper develops an ndimensional markovfunctional interest rate model, i. Semianalytic lattice integration of a markov functional. To achieve this we consider the general class of markov functional interest rate models mf models, first introduced by hunt, kennedy and pelsser 2000. A comparison of markovfunctional and market models. Introduction the ndimensional markovfunctional model pricing tests aim of the paper i develop an ndimensional markovfunctional interest rate model mfm. Forecasting and simulation jel e47, corporate finance and governance jel g3, business. A comparison of single factor markovfunctional and multi. The propagation property can be found implicitly in all of the popular state price density. Onefactor markovfunctional interest rate models and pricing.

We introduce a general class of interest rate models in which the value of pure. We study a markov functional mf interest rate model with uncertain volatility displaced diffusion uvdd digital mapping, which is consistent with the volatilitysmile phenomenon observed in the option market. This paper develops an ndimensional markov functional interest rate model, i. A heat kernel approach to interest rate models springerlink. A comprehensive view of markovfunctional models and their. We demonstrate the speed and accuracy of the method using a markovfunctional interest rate model, also demonstrating how the model greeks can be converted into market greeks. As noted above, mean reversion of interest rates is determined mainly by the function. To achieve this we consider the general class of markovfunctional interest rate models mf models, first introduced by hunt, kennedy and pelsser 2000. The hybrid markovfunctional model extends the singlecurrency interest rate markovfunctional model to a consistent model of the joint evolution of interest rates and another stochastic underlying. Phase transition in a lognormal interest rate model. Pricing models for bermudanstyle interest rate derivatives. Semianalytic lattice integration of a markov functional term.

A major motivation which lead to their development was the desire to have models that can exactly replicate prices of liquid calibration instruments in a similar fashion to market models while maintaining the e. We demonstrate that the onedimensional libor markov functional model and the separable onefactor libor market model are very similar. In particular we develop a stochastic volatility markovfunctional model. Markov functional market model and standard market model. Interest rate models form an important part of the field of quantitative fi nance. Although markovfunctional models are indeed a popular choice in practise introductionandsummary this thesis consists of three papers in the area of interest rate derivatives. Markovfunctional interest rate models the journal of economic. Request pdf markovfunctional interest rate models we introduce a general class of interest rate models in which the value of pure discount bonds can be. We introduce a general class of interest rate models in which the value of pure discount bonds can be expressed as a. We compare single factor markovfunctional and multi factor market models for hedging performance of bermudan swaptions. The class of short rate models is, in fact, a special case of arbitragefree models of the term structure for which the short rate r t t. In this thesis we study lowdimensional stochastic volatility interest rate models for pricing and hedging exotic derivatives.

An example of a cap would be an agreement to receive a payment for each month the libor rate exceeds 2. Fast greeks for markovfunctional models using adjoint pde. Implications for hedging of the choice of driving process for. The three volumes of interest rate modeling are aimed primarily at practitioners working in the area of interest rate derivatives, but much of the material is quite general and, we believe, will also hold significant appeal to researchers working in other asset classes. The dynamics in a markov functional one factor model is given by a one dimensional markovian state variable x. Markovfunctional interest rate models springerlink. Hjm models hullwhite, extended cir, blackkarasinski, squaredgaussian, liritchkensankarasubramanian, bharchiarella libor market models lmm lmm with stochastic volatility lmm with jumps markovfunctional interest rate models huntkennedypellser credit derivatives.

An ndimensional markovfunctional interest rate model. Crosscurrency and hybrid markovfunctional models 1 introduction in this paper we consider crosscurrency markovfunctional models and their calibration under the spot measure. We study a markovfunctional mf interestrate model with uncertain volatility displaced diffusion uvdd digital mapping, which is consistent with the volatilitysmile phenomenon observed in the option market. We then recall the theoretical framework for interest rate models and the heathjarrowmorton framework. We introduce a general class of interest rate models in which the value of pure discount bonds can be expressed as a functional of some lowdimensional markov process. An interest rate cap is a derivative in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed strike price. The libor markovfunctional model is an efficient arbitragefree pricing model suitable for callable interest rate derivatives. A comparison of markovfunctional and market models the. Explicit bond option and swaption formula in heathjarrowmorton one factor model, international journal. We demonstrate that the onedimensional libor markov functional. Simon johnson, commerzbank introduction to markov functional models 1factor markov functional models. We describe the implementation of a markov functional one factor interest rate model in the quantlib 4 framework. Students and academics interested in financial engineering and applied work.

We demonstrate that the onedimensional libor markovfunctional model and the separable onefactor libor market model are very similar. The article works through various approaches and models in a historical sequence. May 17, 2014 we construct defaultfree interest rate models in the spirit of the wellknown markov functional models. Interest rate models theory and practice with smile, inflation and credit 2nd ed. The model is suitable for pricing certain types of exotic interest rate derivative products, such as targeted accrual redemption notes, on libors or constant maturity swap spreads. Markov functional modeling of equity, commodity and other. An additional advantage of markovfunctional models is the fact that the specification of the model can be such that the forward rate distribution implied by market option prices can be fitted exactly, which makes these models particularly suited for derivatives pricing.

The ndimensional markov functional model pricing tests an ndimensional markov functional interest rate model linus kaisajuntti1 joanne kennedy2 1department of finance, stockholm school of economics 2department of statistics, university of warwick july 12, 2008 linus kaisajuntti, joanne kennedy an ndimensional markov functional interest rate. Woodward2 1numerix,546fifthavenue,17thfloor,newyork,ny10036. Markov functional modeling of equity, commodity and other assets christian p. An additional advantage of markov functional models is the fact that the specification of the model can be such that the forward rate distribution implied by market option prices can be fitted exactly, which makes these models particularly suited for derivatives pricing. In particular we develop a stochastic volatility markov functional model. As the second underlying we consider the fx rate, but this could also be. Pertursson, comparison of the hedging performance of bermudan swaptions for different driving processes in the markov functional interest rate model, masters thesis, university of warwick 2008. Next, we also investigate the future smiles implied by the mf models and the smile dynamics implied by the uvdd. Assume that one has the right to enter the swap at the times t 0,t n1, where n. Mathematical finance is the first book to harmonize the theory, modeling, and implementation of todays most prevalent pricing models under one convenient cover.

Phil hunt, joanne kennedy, antoon pelsser markovfunctional. In a single currency economy a markov functional model can. Options on zero coupon bond, capsfloors, swaptions, bermudan swaptions, exotic products affine models hjm models hullwhite, extended cir, blackkarasinski, squaredgaussian, liritchkensankarasubramanian, bharchiarella libor market models lmm lmm with stochastic volatility lmm with jumps markovfunctional interest rate models. Global derivatives and fixed income markets, westdeutsche.

Financial derivatives in theory and practice, revised. It is shown that this model is very similar to an nfactor libor market model hence allowing intuition from the libor market model to be transferred to the markov. We work in the setting of state price densities and construct models by means of the so called propagation property. The largest convexity adjustments are seen for irrforwards referencing long tenors and long expiries. Hunt, kennedy and pelser 11, 9 suggested a markov functional model for this purpose, where the randomness comes through a low dimensional markov process and the interest rates are a functional of this random process. Onefactor markovfunctional interest rate models and. We demonstrate that the onedimensional libor markovfunctional.

For these products, the ndimensional markovfunctional model may be used as a benchmark model, allowing for powerful and flexible control of both correlations. Building a bridge from academia to practice, this selfcontained text applies theoretical concepts to realworld examples and introduces stateoftheart, objectoriented programming. Adjoint pde greeks, delta, vega, skew, adjoint method, pde, markovfunctional model, market greeks, cancellable inverse floater, bermudan swaption. Onefactor markovfunctional interest rate models and pricing of. Markov functional modeling of equity, commodity and other assets. Hunt, kennedy and pelsser 12, 18 introduced a singlecurrency markovfunctional interest rate model in the terminal measure and showed how to ef.

Markov functional interest rate models the class of models with which we shall work we refer to as markov functional interest rate models mf models. Introduction to markov functional models 1factor markov functional models. Although markov functional models are indeed a popular choice in practise introductionandsummary this thesis consists of three papers in the area of interest rate derivatives. This paper develops an ndimensional markov functional interest rate model, ie, a model driven by an ndimensional state process and constructed using markov functional techniques. Markovfunctional model is appropriately calibrated to \terminal correlations of swap rates that are relevant to the bermudan swaption then the hedging performance of both the multifactor and single factor models are comparable. We construct defaultfree interest rate models in the spirit of the wellknown markov functional models. Markovfunctional interest rate models phil hunt1, joanne kennedy2, antoon pelsser3 1 global derivatives and fixed income markets, westdeutsche landesbank, 3336 grace church street, london ec3v 0ax, united kingdom email. The stochastic volatility markovfunctional model wrap.

We first check the impact of pricing bermudan swaptions by the model. Markovfunctional interest rate models finance and stochastics, 4, 391408 2000 3 a. It contains the key points that can be found in the present literature. In order to implement the model numerically, we further propose a general algorithm by working with basis functions and conditional moments of the driving markov process. Multidimensional markovfunctional and stochastic volatility. Partly this is for historys sake, but, more importantly, the older models are simpler and easier to understand. The term financial derivative is a very broad term which has come to mean any financial transaction whose value depends on the underlying value of the asset concerned. Markov functional models are well known in interest rate 7 and interest rate hybrid modeling 5. It is shown that this model is very similar to an nfactor libor market model, thus allowing intuition from the libor market model to be transferred to the markov. Explicit bond option and swaption formula in heathjarrowmorton one factor model, international journal of theoretical and applied finance, 61, 5772.

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