The Pricing of Tail Risk and the Equity Premium: Evidence From International Option Markets

We examine the pricing of financial crash insurance during the 2007–2009 financial crisis in US option markets, and we show that a large amount of aggregate tail risk is missing from the cost of financial sector crash insurance during the crisis. The difference in costs between out-of-the-money put options for individual banks and puts on the financial sector index increases four-fold from its precrisis 2003–2007 level. We provide evidence that a collective government guarantee for the financial sector lowers index put prices far more than those of individual banks and explains the increase in the basket-index put spread. (JEL E44, G01, G13, G21, G28, H81)

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Idiosyncratic Jump Risk Matters: Evidence from Equity Returns and Options

Review of Financial Studies ◽

10.1093/rfs/hhz043 ◽

2019 ◽

Vol 33 (1) ◽

pp. 155-211 ◽

Cited By ~ 10

Author(s):

Jean-François Bégin ◽

Christian Dorion ◽

Geneviève Gauthier

Keyword(s):

Risk Premium ◽

Recent Literature ◽

Equity Premium ◽

Idiosyncratic Risk ◽

Equity Returns ◽

Jump Risk ◽

Tail Risk ◽

Oxford University ◽

Editorial Decision ◽

Published Paper

Abstract The recent literature provides conflicting empirical evidence about the pricing of idiosyncratic risk. This paper sheds new light on the matter by exploiting the richness of option data. First, we find that idiosyncratic risk explains 28% of the variation in the risk premium on a stock. Second, we show that the contribution of idiosyncratic risk to the equity premium arises exclusively from jump risk. Third, we document that the commonality in idiosyncratic tail risk is much stronger than that in total idiosyncratic risk documented in the literature. Tail risk thus plays a central role in the pricing of idiosyncratic risk. Received May 15, 2017; editorial decision September 12, 2018 by Editor Stijn Van Nieuwerburgh. Authors have furnished code and an Internet Appendix, which are available on the Oxford University PressWeb site next to the link to the final published paper online.

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Estimation of Tail Risk and Moments Using Option Prices with a Novel Pricing Model under a Distorted Lognormal Distribution

Mathematical Problems in Engineering ◽

10.1155/2020/1603509 ◽

2020 ◽

Vol 2020 ◽

pp. 1-25

Author(s):

Yan Chen ◽

Ya Cai ◽

Chengli Zheng

Keyword(s):

Lognormal Distribution ◽

Risk Measures ◽

Empirical Test ◽

Asset Price ◽

Test Results ◽

Option Prices ◽

Tail Risk ◽

Option Markets ◽

Novel Method ◽

Real Market

Risk measures based on the trading option prices in the market are forward-looking, such as VIX. We propose a new method combining distorted lognormal distribution with interpolation to price options accurately and then estimate tail risk. Our method can price the option of any strikes between the maximum and the minimum value of strikes in the real market, which reduces the instability and inaccuracy of using the limited option to measure the risk. In addition, our novel method treats the underlying asset price as a stochastic indicator rather than a fixed indicator as described in previous research studies for risk measurement. Moreover, even if the available sample size is very small, we can measure the risk stably and precisely after interpolation. Finally, the empirical test results of SP500 market show that this method has good performance, especially for the option markets with sparse strikes.

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