scholarly journals Robust calibration and arbitrage-free interpolation of SSVI slices

2019 ◽  
Vol 42 (2) ◽  
pp. 665-677 ◽  
Author(s):  
Jacopo Corbetta ◽  
Pierre Cohort ◽  
Ismail Laachir ◽  
Claude Martini
Keyword(s):  
Free Interpolation

scholarly journals Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 30
Author(s):  
Fabien Le Floc’h ◽  
Cornelis Oosterlee
Keyword(s):  
Implied Volatility ◽  
Initial Guess ◽  
Stochastic Collocation ◽  
Option Prices ◽  
Spline Collocation ◽  
Model Free ◽  
Free Interpolation ◽  
Collocation Technique ◽  
Interpolation Technique ◽  
The Stability

This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how to smooth out the market quotes, and choose a proper initial guess. The technique is then applied to concrete market options and the stability of the different approaches is analyzed. Finally, we consider a challenging example where convex spline interpolations lead to oscillations in the implied volatility and compare the spline collocation results with those obtained through arbitrage-free interpolation technique of Andreasen and Huge.

scholarly journals Error-Free Interpolation of Parametric Surfaces

1992 ◽  
Vol 114 (3) ◽  
pp. 271-276 ◽  
Author(s):  
J. G. Gan ◽  
T. C. Woo
Keyword(s):  
Cost Effective ◽  
Parametric Surfaces ◽  
Parametric Curves ◽  
Acceptable Limit ◽  
Effective Implementation ◽  
Curves And Surfaces ◽  
Free Interpolation ◽  
Minimum Number ◽  
Differential Analyzer

A Digital Differential analyzer (DDA) is a cost effective implementation for interpolating parametric curves and surfaces. However, the problems of register overflow and integer round-off have prevented it from being adopted by industry. Contrary to intuition, an increase in register capacity is shown to have no bearing on the register overflow problem. It is shown that there is a minimum number of interpolation steps Kl below which register overflow occurs. Correspondingly, it is also shown that there exists a maximum number of interpolation steps Ku above which the accumulation of integer round-off errors exceeds the acceptable limit. But, when Kl>Ku, conflict arises. A solution is given to resolve the possible conflict and to yield an error-free interpolation of curves and surfaces.

ARBITRAGE-FREE INTERPOLATION OF THE SWAP CURVE

2009 ◽  
Vol 12 (07) ◽  
pp. 969-1005 ◽  
Author(s):  
MARK H. A. DAVIS ◽  
VICENTE MATAIX-PASTOR
Keyword(s):  
Closed Form ◽  
Yield Curve ◽  
Interpolation Method ◽  
Continuous Process ◽  
Closed Form Solution ◽  
Form Solution ◽  
Market Model ◽  
Short Term ◽  
Free Interpolation ◽  
Swap Rates

We suggest an arbitrage free interpolation method for pricing zero-coupon bonds of arbitrary maturities from a model of the market data that typically underlies the swap curve; that is short term, future and swap rates. This is done first within the context of the Libor or the swap market model. We do so by introducing an independent stochastic process which plays the role of a short term yield, in which case we obtain an approximate closed-form solution to the term structure while preserving a stochastic implied short rate. This will be discontinuous but it can be turned into a continuous process (however at the expense of closed-form solutions to bond prices). We then relax the assumption of a complete set of initial swap rates and look at the more realistic case where the initial data consists of fewer swap rates than tenor dates and show that a particular interpolation of the missing swaps in the tenor structure will determine the volatility of the resulting interpolated swaps. We give conditions under which the problem can be solved in closed-form therefore providing a consistent arbitrage-free method for yield curve generation.

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