Empirical tests of canonical nonparametric American option‐pricing methods

Alcock, Jamie; Auerswald, Diana

doi:10.1002/fut.20421

Cited by 18 publications

(20 citation statements)

References 19 publications

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“…We also estimate prices generated by the Pearson's chi-square (CHI) divergencebased scheme, and by a naive model (CONST) that uses constant probabilities of 1/N in the general pricing formula (4) instead of using risk-neutral probabilities. Using the same bootstrap, we then estimate the riskneutral probability measures by the minimization problem (8) for each given model, and 3 This is consistent with previous empirical studies of nonparametric pricing methods (Alcock & Auerswald, 2010;Gray, Edwards, & Kalotay, 2007). We compare the price estimates from each pricing model to the actual market traded price across all filtered option trades to generate mean dollar pricing error (MDE) for various levels of moneyness and time-to-expiry.…”

Section: Pricing Methodologymentioning

confidence: 73%

“…This simple technique of choosing the constraining options differs slightly from that used by Gray, Edwards, and Kalotay (2007) and by Alcock and Auerswald (2010), but results in a larger usable sample and in significant improvements in pricing performance. The constrained models each use two additional pricing constraints that ensure that they accurately price the most recently traded European call and put options from the same moneyness/time-toexpiry subset as the given option being priced (the first option trade of a given sample is thus not used in the calculation of the pricing performance statistics).…”

Section: Pricing Methodologymentioning

confidence: 99%

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Testing Alternative Measure Changes in Nonparametric Pricing and Hedging of European Options

Alcock

Smith

2013

Journal of Futures Markets

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Haley and Walker [Haley, M.R., & Walker, T. (2010). Journal of Futures Markets, 30, 983–1006] present the Euclidean and Empirical Likelihood nonparametric option pricing models as alternative tilts to Stutzer's [Stutzer, M. (1996). Journal of Finance, 51, 1633–1652] Canonical pricing method. We empirically test the comparative strengths of each of these methods using a large sample of traded options on the S&P100 Index. Furthermore, we explore an additional tilt based on Pearson's chi‐square, and derive and empirically test nonparametric delta hedges for each of these approaches. Differences in the pricing performance of the various tilts are a function of differences between the sample distribution and the real distribution of the underlying. When the sample distribution displays fatter (thinner) tails and/or higher (lower) volatility than the true distribution, the Euclidean (Pearson's chi‐square) model outperforms. Significantly, when these nonparametric methods utilize information contained in a small number of observed option prices they often outperform the implied volatility Black and Scholes [Black, F., & Scholes, M. (1973). Journal of Political Economy, 81, 637–654] model. These pricing performance differences do not translate into static and dynamic hedging performance differences. However, each of the nonparametric models induce an implied volatility smile and term structure that generally agree in form with the smile and term structure embedded in market prices. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:320–345, 2014

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Section: Pricing Methodologymentioning

confidence: 73%

Section: Pricing Methodologymentioning

confidence: 99%

Testing Alternative Measure Changes in Nonparametric Pricing and Hedging of European Options

Alcock

Smith

2013

Journal of Futures Markets

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“…The estimated riskneutral transition density is then used to price the option itself by the algorithm (see also Liu [2010]). Alcock and Auerswald [2010] consider the same approach and add the no-arbitrage restrictions on a cross section of observed European options. Duan [2002] considers the series of returns on the underlying and divides the difference between each return and the conditional mean by the conditional volatility.…”

Section: Model Calibration and Empirical Methodsmentioning

confidence: 99%

Semi-parametric estimation of American option prices

Gagliardini

Ronchetti

2013

Journal of Econometrics

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An American option provides the right to perform a specified financial transaction (sell, buy, exchange) on or before the contract maturity. Many different contracts traded on centralized and OTC markets are of this kind. In particular, a plain vanilla American option is a contract between two parties concerning the possibility of selling or buying a reference asset (underlying) at a specified price (strike price). Setting the contract price and choosing the best moment for its exercise are two of the most studied problems in finance during the last 40 years. In financial markets, the behavior of the underlying is not predictable. Thus, a description of the probability law governing its stochastic evolution is necessary for the determination of the contract price and the optimal exercise decision.The majority of the existing literature focuses on mathematical and numerical procedures for computing the option price and determining the optimal exercise policy for a given law of motion of the underlying. For these purposes, only a model for the dynamics of the underlying under the risk-neutral distribution is required. When this approach is put into practice, typically a parametric model for such distribution is adopted and the parameters are calibrated on a cross-section of available option prices.On the contrary, in this PhD thesis, that summarizes the research conducted to obtain the degree of Doctor of Philosophy in Economics at the University of Lugano, an econometric framework for the empirical pricing of American options is developed. In this framework, a statistical model for the dynamics of the underlying is specified by the researcher and estimated on available data. Data include both time series of relevant state variables and cross-sections of observed option prices. The estimated model is then used to estimate the price of contracts that are not currently actively traded on the market.The econometric approach proposed in this thesis features three major characteristics. First, it is based on a coherent specification of both historical and risk-neutral dynamics. Second, the statistical model for the dynamics of the underlying is more general than most of the models previously considered in the literature. Third, the model parameters can be consistently estimated even when the amount of option data is limited.In the first three chapters of the thesis, the problem, the proposed solution and an empirical application of the novel method are presented. Chapter 1 introduces the price of an American option as the expected value of the contract at the most remunerative time for exercising it. Some different pricing techniques based on this representation and the way they are used to handle with real data are briefly reviewed. Chapter 2 presents the novel empirical methodology developed in the PhD research.Chapter 3 describes an application of this methodology for the analysis of IBM shares and plain vanilla American options written on them. In the last two chapters of the thesis, the regularity assumptions

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“…Results suggest that canonical valuation has merits in both applications. Further extensions of canonical valuation have been considered by Alcock and Carmichael (2008), Alcock and Auerswald (2010), Haley and Walker (2010), and Liu (2010).…”

Section: Figurementioning

confidence: 98%

On the calibration of mortality forward curves

Chan

2010

J. Fut. Mark.

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In 2007, a major investment bank launched a product called "q-forward," which may be regarded as a forward contract on a mortality rate. The pricing of mortality forwards is similar to the pricing of other forward-rate contracts, such as interest-rate forwards or foreign exchange forwards. In particular, since investors require compensation to take on longevity risk, the forward mortality rate at which q-forward contracts will trade will be smaller than the expected mortality rate. The relationship between the forward rate and the time to maturity is called a mortality forward curve. In this study, we contribute a method for calibrating mortality forward curves. This method consists of two parts, one of which is the generation of the distribution of future mortality rates, and the other of which is the transformation of the distribution into its risk-neutral counterpart, using the idea of canonical valuation developed by Stutzer, M. (1996). To illustrate the method,

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Empirical tests of canonical nonparametric American option‐pricing methods

Cited by 18 publications

References 19 publications

Testing Alternative Measure Changes in Nonparametric Pricing and Hedging of European Options

Testing Alternative Measure Changes in Nonparametric Pricing and Hedging of European Options

Semi-parametric estimation of American option prices

On the calibration of mortality forward curves

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