[PDF] A Robust Method To Retrieve Option Implied Risk Neutral Densities For Defaultable Assets eBook

Author : Guillaume Leduc
Publisher :
Page : 17 pages
File Size : 30,14 MB
Release : 2017
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Risk neutral densities recovered from option prices can be used to infer market participantsņ expectations of future stock returns and are a vital tool for pricing illiquid exotic options. Although there is a broad literature on the subject, most studies do not address the likelihood of default. To fill this gap, in this paper we develop a novel method to retrieve the risk neutral probability density function from call options written on a defaultable asset. The primary advantage of the method is that default probabilities inferred by the model can be analytically expressed and, if available, can be incorporated as an input in a ፟lexible, robust and easily implementable manner.

Author : Stephen Figlewski
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Page : 44 pages
File Size : 40,36 MB
Release : 2012
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The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technical problems arise. In order to obtain a full well-behaved density, the option market prices must be smoothed and interpolated, and some way must be found to complete the tails beyond the range spanned by the available options. This paper develops an approach that solves both problems, with a combination of smoothing techniques from the literature modified to take account of the market's bid-ask spread, and a new method of completing the density with tails drawn from a Generalized Extreme Value distribution. We extract twelve years of daily risk neutral densities from Samp;P 500 index options and find that they are quite different from the lognormal densities assumed in the Black-Scholes framework, and that their shapes change in a regular way as the underlying index moves. Our approach is quite general and has the potential to reveal valuable insights about how information and risk preferences are incorporated into prices in many financial markets.

Author : Allan M. Malz
Publisher :
Page : 42 pages
File Size : 21,15 MB
Release : 2014
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This paper describes a method for computing risk-neutral density functions based on the option-implied volatility smile. Its aim is to reduce complexity and provide cookbook-style guidance through the estimation process. The technique is robust and avoids violations of option no-arbitrage restrictions that can lead to negative probabilities and other implausible results. I give examples for equities, foreign exchange, and long-term interest rates.

Author : Greg Orosi
Publisher :
Page : 6 pages
File Size : 50,75 MB
Release : 2015
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This paper provides an improved model-independent lower bound of European call options written on defaultable assets. Based on static arbitrage arguments, improved lower bounds are established, which also depend on the probability of option implied default. The results are also extended to dividend paying stocks. Moreover, our findings imply that it is never optimal to exercise certain American call options. Finally, we discuss the implications of our results for constructing an arbitrage-free volatility surface and extracting risk-neutral densities from option prices.

Author : Oleg Bondarenko
Publisher :
Page : 61 pages
File Size : 19,20 MB
Release : 2008
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This paper proposes a novel nonparametric method to recover the implied risk-neutral density (RND) from option prices. The main advantages of this method are that it 1) is almost completely agnostic about the true underlying process, 2) controls against overfitting while allowing for small samples, 3) always results in sensible arbitrage-free distributions, 4) estimates the RND over the observable range of strikes only, without involving any extrapolation of density in the tails, 5) is computationally very simple, and 6) can be used to estimate multivariate RNDs. In an empirical application, the new method is implemented on the Samp;P Index options data over the period from 1991 to 1995. To characterize shapes of the Index's RNDs the paper uses the percentile moments which overcome unobservability of the tails of a distribution. The implied RNDs exhibit persistent negative skewness and excessive peakedness. The departures from lognormality become more pronounced as option maturity increases. Day-to-day variation of the RNDs is found to be related to the recent performance of the Index. In particular, on trading days when the Index declines the implied RNDs are more skewed and peaked than when the Index advances. Finally, the implied probabilities of extreme outcomes are also estimated.

Author : James Huang
Publisher :
Page : 32 pages
File Size : 48,56 MB
Release : 2009
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In this paper we raise a question on the theoretical foundation of option implied risk neutral density. We prove that given any number of options, there exist numerous risk neutral densities which are piecewise constant, have only two values, either an lower bound or an upper bound on the true risk neutral density, and price all these options correctly. We also prove that given any number of options, there exist numerous risk neutral densities consistent with the prices of all these options whose first derivatives are piecewise constant and have only two values, either an lower bound or an upper bound on the true risk neutral density's first derivative. Similar results are proved with respect to the true risk neutral density's higher order derivatives. These results show how large errors we can make when extracting RNDs from option prices.