The Price of the Smile and Variance Risk Premia

70 Pages Posted: 18 Sep 2015 Last revised: 25 Sep 2015

See all articles by Peter H. Gruber

Peter H. Gruber

University of Lugano - Institute of Finance

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance; Bocconi University - Department of Finance; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Fabio Trojani

Swiss Finance Institute; University of Geneva

Date Written: September 8, 2015

Abstract

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance risk premia in normal times. In periods of distress, the term structure is upward sloping and dominated by a high-frequency premium for jump variance. This dichotomy is consistent with the puzzling skew sensitivities of option markets with credit-constrained intermediaries and it builds a challenge for many reduced-form and structural models of stochastic volatility.

Keywords: Price of the Smile, Price of Volatility, Option Pricing, Stochastic Volatility, Unspanned Skewness, Financial Constrains, Financial Intermediation, Financial Crisis, Factor Models, Matrix Jump Diffusions, Variance Swaps, Skew Swaps

JEL Classification: G10, G12, G13

Suggested Citation

Gruber, Peter H. and Tebaldi, Claudio and Trojani, Fabio, The Price of the Smile and Variance Risk Premia (September 8, 2015). Swiss Finance Institute Research Paper No. 15-36. Available at SSRN: https://ssrn.com/abstract=2648288 or http://dx.doi.org/10.2139/ssrn.2648288

Peter H. Gruber (Contact Author)

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance ( email )

Via Roentgen 1
Milan, 20136
Italy

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

Via Roentgen 1
Milan, 20136
Italy

Fabio Trojani

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva
Switzerland

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