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Author: Gregory Pelts
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
For the last decade, short-term rates of major currencies were consistently low and occasionally negative. Meanwhile, longer-term rates remained relatively high and volatile. This phenomenon added extra complexity to the the already formidably difficult task of pricing and hedging interest rate derivatives, rendering conventional approaches virtually defunct. We have observed that the application of jump diffusion in conjunction with conformal geometry allows to successfully tackle such market behavior in a fully consistent, tractable, and computationally efficient manner. The approach provides explicit parametric yield curves with arbitrage-free dynamics, and, in certain cases, even closed-form formulae for yield distributions. This is achieved without compromising efficiency or calibration flexibility. In particular, the 4D version of the model has been successfully calibrated to the swaption market with acceptable precision. The methodology has been applied in valuation of various exotic interest rate derivatives.
Author: Gregory Pelts
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
For the last decade, short-term rates of major currencies were consistently low and occasionally negative. Meanwhile, longer-term rates remained relatively high and volatile. This phenomenon added extra complexity to the the already formidably difficult task of pricing and hedging interest rate derivatives, rendering conventional approaches virtually defunct. We have observed that the application of jump diffusion in conjunction with conformal geometry allows to successfully tackle such market behavior in a fully consistent, tractable, and computationally efficient manner. The approach provides explicit parametric yield curves with arbitrage-free dynamics, and, in certain cases, even closed-form formulae for yield distributions. This is achieved without compromising efficiency or calibration flexibility. In particular, the 4D version of the model has been successfully calibrated to the swaption market with acceptable precision. The methodology has been applied in valuation of various exotic interest rate derivatives.
Author: Gregory Pelts
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
We employ conformal symmetries to provide a generic tractable framework for interest rate modelling. The approach combines calibration flexibility of market models with tractability and computational efficiency of shot rate models. The methodology enables robust calibration to the whole variety of caps and swaptions with various expirations, strikes and tenors. In the same time, low dimensionality enables backward induction allowing efficient valuation of bermudan swaptions without resorting to suboptimal American Monte Carlo.
Author: Gregory Pelts
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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Book Description
Volatility is called unspanned if it can be dynamically separated from analytical representation of the underlying observables, such as swap or market rates. This quality is paramount for efficient calibration and pricing. Conformal symmetries provide a powerful tool for building parsimonious models of this kind. However, in this family of models, only common scale of volatility is unspanned. This limits the model calibration flexibility, particularly, in the low rate regime. Here, we demonstrate how to overcome these restrictions. This is achieved via application of projective geometry and abstract algebra.
Author: Robert Josef Stelzer
Publisher:
ISBN:
Category :
Languages : en
Pages : 249
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Author: Ole E. Barndorff-Nielsen
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Category :
Languages : en
Pages :
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Author: Lu Feng
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Category : Stochastic processes
Languages : en
Pages : 228
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Author: Adriana Ocejo Monge
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Category :
Languages : en
Pages : 0
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Author: Joann Jasiak
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Category :
Languages : en
Pages :
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In this paper, we study stochastic volatility models with time deformation. Such processes relate to the early work by Mandelbrot and Taylor (1967), Clark (1973), Tauchen and Pitts (1983), among others. In our setup, the latent process of stochastic volatility evolves in an operational time which differs from calendar time. The time deformation can be determined by past volume of trade, past returns, possibly with an asymmetric leverage effect, and other variables setting the pace of information arrival. The econometric specification exploits the state-space approach for stochastic volatility models proposed by Harvey, Ruiz and Shephard (1994) as well as the matching moment estimation procedure using SNP densities of stock returns and trading volume estimated by Gallant, Rossi and Tauchen (1992). Daily data on returns and trading volume of the NYSE are used in the empirical application. Supporting evidence for a time deformation representation is found and its impact on the behavior of returns and volume is analyzed. We find that increases in volume accelerate operational time, resulting in volatility being less persistent and subject to shocks with a higher innovation variance. Downward price movements have similar effects while upward price movements increase the persistence in volatility and decrease the dispersion of shocks by slowing down market time. We present the basic model as well as several extensions; in particular, we formulate and estimate a bivariate return-volume stochastic volatility model with time deformation. The latter is examined through bivariate impulse response profiles following the example of Gallant, Rossi and Tauchen (1993).
Author: Guojing Tang
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ISBN:
Category :
Languages : en
Pages :
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Author: Kyriakos M. Chourdakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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