Known as a new standard in the financial industry, HN model is used as reference model to test the forecast results of four option pricing models
created in this paper.
Although volatility forecasts have many practical applications such as the use in the analysis of market timing decisions, aid with portfolio selection and the provision of estimates of variance for use in option pricing models
, in our study we are not trying to find the predictive ability of various models but the intertemporal relationship between the forecasts of different nature.
The rest of paper is arranged as follows: In Section 2 we describe the American option pricing models
with time-fractional derivatives; in Section 3 we introduce the Laplace transform methods for the problem; in Section 4 we give the boundary-searching finite difference methods for the problem; in Section 5 we provide numerical examples to compare the performance of the Laplace transform method with FDM; the conclusions are made in the final section.
Financial option pricing models
have long been employed to evaluate the equity and debt values of financial institutions (e.g., Merton, 1977; Furlong and Keeley, 1989; Doherty and Garven, 1986; Cummins, 1988a, 1988b; Cummins et al., 1999; Ibragimov et al., 2010).
Vetzal, "A general finite element approach for PDE option pricing models
El-Hassan, "The calibration of stock option pricing models
using inverse problem methodology," QFRQ Research Papers, University of Technology, Sydney, Sydney, Australia, 2000.
By relaxing some of the restrictive assumptions, such as the assumption of constant volatility and the geometric Brownian motion for the price of the underlying asset, many option pricing models
have been proposed.
Bezdek, "Numerical solutions for option pricing models
including transaction costs and stochastic volatility," Acta Applicandae Mathematicae, vol.
* "Our experience, which includes working with over 1,500 companies over a period of 31 years, indicates that traditional option pricing models
tend to overstate the value of employee options.
However, outside of the consulting function, it would seem that option valuation theory or the development of option pricing models
would be well beyond the practice of most real estate appraisers for a number of reasons.
Subjects include: derivative markets and instruments, options market structures, option pricing models
and strategies, the structure of forward and futures markets, futures arbitrage strategies, swaps, financial risk management techniques and applications, and managing risk in organizations.
This reflects the fact that companies value option grants based on option pricing models
(usually the Black-Scholes model), and the value of a newly granted option is considerably less than the value of a share of stock.[double dagger]