Pricing American options by canonical least‐squares Monte Carlo

Liu, Qiang

doi:10.1002/fut.20409

Cited by 14 publications

(23 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alcock and Carmichael [2008] adopts the canonical valuation methodology with no-arbitrage restrictions on an American option at every possible exercise date. 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.…”

Section: Model Calibration and Empirical Methodsmentioning

confidence: 99%

Semi-parametric estimation of American option prices

Gagliardini

Ronchetti

2013

Journal of Econometrics

View full text Add to dashboard Cite

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

show abstract

Section: Model Calibration and Empirical Methodsmentioning

confidence: 99%

Semi-parametric estimation of American option prices

Gagliardini

Ronchetti

2013

Journal of Econometrics

View full text Add to dashboard Cite

show abstract

“…As is reasoned in Liu (2010) for GBM, the canonical distribution and its implied binomial tree, if correct, should price European options and American calls exactly as the Black-Scholes (BS) formulas do. Furthermore, the CIB approach should match CLM (Liu, 2010) for American puts. More importantly, the estimated canonical distribution should be independent of the growth rate of the GBM model.…”

Section: Numerical Experimentsmentioning

confidence: 98%

“…For ease of comparison, the same set of parameters for options is taken directly from Liu (2010) • Risk-free interest rate: 6.0% Further, we simulated underlying prices under GBM in two cases: drift parameters of 6% (the risk-neutral case) and 100% (an extreme case), which follow Liu (2010) exactly.…”

Section: Numerical Examplementioning

confidence: 99%

See 1 more Smart Citation

Canonical Distribution, Implied Binomial Tree, and the Pricing of American Options

Liu

Guo

2011

Journal of Futures Markets

Self Cite

View full text Add to dashboard Cite

Jun Liu is thanked for encouraging this research from the very beginning, and Chong Jiang is thanked for bringing the implied binomial tree method to Qiang's attention. The authors are truly grateful to the anonymous reviewer for suggesting the inclusion of hedging performance in the study, for helping improve the scholarship of the study in numerous ways, and for expediting the review process. The editorial support from Editor Robert Webb is sincerely appreciated without any reservation.

show abstract

“…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.

View full text Add to dashboard Cite

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,

show abstract

Pricing American options by canonical least‐squares Monte Carlo

Cited by 14 publications

References 11 publications

Semi-parametric estimation of American option prices

Semi-parametric estimation of American option prices

Canonical Distribution, Implied Binomial Tree, and the Pricing of American Options

On the calibration of mortality forward curves

Contact Info

Product

Resources

About