A Simple Nonparametric Approach to Derivative Security Valuation

Stutzer, Michael J.

doi:10.2307/2329532

Cited by 171 publications

(217 citation statements)

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“…Buchen and Kelly [3] investigated the use of the principle of maximum entropy to the estimation of the distribution for the underlying assets from a set of market option data. Stutzer [40] studied the problem of derivative valuation using a simple non-parametric approach based on the MEMM. Avellaneda [1] presented an algorithm for calibrating asset pricing models to benchmark prices by minimizing relative entropy with respect to a prior distribution.…”

Section: Regime Switching Esscher Transform and Relative Entropymentioning

confidence: 99%

Option pricing and Esscher transform under regime switching

2005

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Section: Regime Switching Esscher Transform and Relative Entropymentioning

confidence: 99%

Option pricing and Esscher transform under regime switching

2005

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“…This can be straighforwardly done based on a probability density function estimation method relying on knowledge of the moments of this density. The method (principle) of maximum entropy constitutes a natural choice for this exercise (Stutzer 1996;Rockinger and Jondeau 2002;Rompolis 2010, for financial applications of this method). This method exploits a number of moment conditions up to order M in deriving a probability density function.…”

Section: Rndmentioning

confidence: 99%

Retrieving risk neutral moments and expected quadratic variation from option prices

Rompolis

Tzavalis

2016

Rev Quant Finan Acc

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This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange.

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“…The main idea is to recover risk-neutral distribution using a nonparametric deterministic volatility function while maintaining that the derivative pricing function is given by the parametric BS formula. Next, we will see a maximum entropy approach initiated by Buchen and Kelly (1996) and Stutzer (1996) to recover a risk-neutral distribution from a set of option and stock prices, as well as the implied binomial tree method of Derman and Kani (1994), Dupire (1994), or Rubinstein (1994). Third, we will survey the purely nonparametric approaches such as kerned-based techniques or learning networks used to estimate an option pricing function and recover the other quantities of interest with option price data.…”

Section: Nonparametric Approachesmentioning

confidence: 99%

“…(5.12) Stutzer (1996) uses this methodology to evaluate the impact of the 1987 crash on the risk-neutral probabilities first using only S&P 500 returns. As many other papers, he finds that the left-hand tail of the canonical distribution estimated with data including the crash extends further than the tail of the distribution without crash data.…”

Section: Canonical Valuation and Implied Binomial Treesmentioning

confidence: 99%