SOLUTION OF THE EXTENDED CIR TERM STRUCTURE AND BOND OPTION VALUATION

The extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these unsolved stochastic differential equations (s.d.e.s) in terms of functionals of their driving Brownian motion and parameters. It is shown that quadratics in solution of linear s.d.e.s solve the ECIR model if and only if the dimension of the model is a positive integer and that this solution can be achieved by construction of a pathwise unique generalized Ornstein-Uhlenbeck process from the ECIR Brownian motion. For real valued dimensions an extension of the time-change theorem of Dubins and Schwarz (1965) is presented and applied to show that a lognormal process solves the model through a stochastic time change. Pathwise equivalence to a rescaled time-changed Bessel square process is also established. These novel results are applied to characterize zero-hitting time and to produce transition density and zero-hitting conditions for the ECIR spot rate. the CIR term structure is then extended to ECIR under no arbitrage, and its solutions and the transition density are represented under a new ECIR martingale measure. the findings are employed to derive a closed-form ECIR bond option valuation formula which generalizes that obtained by CIR (1985).     

Qualitative analysis of the process of restoring social esteem by the women with multiple sclerosis

The present study has been conducted with the purpose of analyzing the process of restoring the social esteem of the women with multiple sclerosis (MS) in the Iranian society through the approach of grounded theory. To this end, a number of 10 women with MS who had referred to Sina Hospital and Iranian MS Society were selected through theoretical sampling. The data collection was conducted through semi-structured interview, on-field note taking, investigating the documents, and memoing. Based on analyzing data, six processes emerged which, according to the order of occurrence, are: (1) seeking and finding treatment, (2) change of the perceived social esteem, (3) struggle to preserve or regain possessions, (4) seeking support and sponsorship, (5) attempt to achieve a desirable consistency, and ultimately, (6) restoring social esteem. The results obtained from this study indicated that though a considerable number of the cases feel changes in their social esteem due to rejection, being abandoned by their spouses, emergence of a co-wife, feeling of burden, financial shortages, and divorce, depending on interventional and contextual conditions including belief in spirituality and supernatural, patient and society’s awareness of the nature of the disease, and the extent of social support, they have experienced varied circumstances. Ultimately, a central level titled “repeated and recurring adjustment of goals” was proposed to reflect the process of restoring the social esteem of the women with MS in Iran.     

EXACT SOLUTION OF A MARTINGALE STOCHASTIC VOLATILITY OPTION PROBLEM AND ITS EMPIRICAL EVALUATION

Exact explicit solution of the log-normal stochastic volatility (SV) option model has remained an open problem for two decades. In this paper, I consider the case where the risk-neutral measure induces a martingale volatility process, and derive an exact explicit solution to this unsolved problem which is also free from any inverse transforms. A representation of the asset price shows that its distribution depends on that of two random variables, the terminal SV as well as the time average of future stochastic variances. Probabilistic methods, using the author's previous results on stochastic time changes, and a Laplace–Girsanov Transform technique are applied to produce exact explicit probability distributions and option price formula. The formulae reveal interesting interplay of forces between the two random variables through the correlation coefficient. When the correlation is set to zero, the first random variable is eliminated and the option formula gives the exact formula for the limit of the Taylor series in Hull and White's (1987) approximation. The SV futures option model, comparative statics, price comparisons, the Greeks and practical and empirical implementation and evaluation results are also presented. A PC application was developed to fit the SV models to current market prices, and calculate other option prices, and their Greeks and implied volatilities (IVs) based on the results of this paper. This paper also provides a solution to the option implied volatility problem, as the empirical studies show that, the SV model can reproduce market prices, better than Black–Scholes and Black-76 by up to 2918%, and its IV curve can reproduce that of market prices very closely, by up to within its 0.37%.