International Journal of Theoretical and Applied Finance

We investigate finite element discretizations using functions that are discontinuous in time and continuous in space for European options with local volatility Black–Scholes models. We present an a posteriori error estimate where a user-specified functional of the error is controlled by the inner product of the finite element residual with the solution of a dual problem that involves the density of the target functional as prescribed data. Examples of error functionals are discussed in the context of either option pricing or volatility calibration from market data. The a posteriori error estimator is then localized onto the space-time cells of the computational mesh and implemented in the framework of an adaptive mesh refinement/derefinement algorithm which provides some form of optimal compromise between accuracy requirements and computational costs. Numerical examples illustrate the efficiency of the proposed methodology.

We present conditions that allow consistent exponential-polynomial forward curve models with two exponential terms to have more than one nontrivial factor. This result leads to seven- and nine-parameter extensions of the Svensson model, for which the consistency conditions allow for two and three stochastic parameters respectively.

This paper provides a structural valuation model for exchangeable convertible bonds, since such bonds are widespread by now. The model is solved through the Hopscotch finite difference method. As the issuer owns the underlying shares, exchangeable convertibles may be called and the exchange option may be exercised even as the issuer experiences financial distress. The value of exchangeable convertibles always decreases in the volatility of the issuer's assets (unlike the value of ordinary convertibles) and decreases in the correlation between the underlying shares and the issuer's assets. The analysis confirms that the dominant motive for issuing exchangeable convertibles is likely to be to dispose of the underlying shares.

An empirical analysis of the Romanian emerging stock market RASDAQ based on the statistical study of the composite index RASDAQ-C reveals the leptokurtic profile of the probability density function (p.d.f.) of the stock index changes, the power law asymptotic behaviour of the p.d.f., the breakdown of scaling at long time scales, the absence of linear correlation in the stock index changes but existence of long-range correlation in nonlinear function such as the absolute value or the square of index changes (implicitly the long-range correlation in the index volatility). These results, consistent with the similar referring to the more liquid markets, suggest the presence of several universal features, in addition to several particularities related to the quickness of assimilation of the new information and its impact over the investors.

The capital structure of a firm is composed of equity and debt. In the Merton approach, equity holders hold a call option on the firm value, while bond holders are short a put on the firm value. Dividends paid to holders of equity provide them with current cash flow. The pay out of dividends to the equity holders devalues a firms debt since it increases its probability of default. With dividend yields at multi-decade lows it seems likely then that in the future some companies that do not currently issue dividends will begin paying dividends and some companies that currently only pay a small dividend will increase their dividend yield. Hence holders of the bonds for a firm that does not presently pay dividends (or pays a small dividend) have "dividend risk" associated with the possibility that at some time in the future the company will start issuing dividends to its stock holders (or increase its dividend rate if it currently pays a small dividend). In this paper we explore the consequences of future dividend increases for bond prices and default probabilities.

The paper provides a continuous time model for order-driven stock market. The model allows to derive a nonlinear PDE as a modification of Black–Scholes equation for option pricing with a local volatility as a function of the stock price. The solution can be expanded in series in the parameter, which relates to the size of option market. The first-order correction for the option price increases the price of a European call. The second-order correction for volatility allows to describe the "volatility smile".

This paper presents a general approach to deriving valuation models and the relevant cost of capital formulas independent of a particular tax environment. The value of a levered firm depends to a large extent upon the amount and value of the tax shields. The latter in turn differs from country to country and even from firm to firm, depending on its particular situation. It is subject to change with every change in the tax system of the country where the firm is located. Therefore, in an international environment a general approach is needed, which can be altered for any given situation. At the same time personal taxes play an increasing role in the valuation of companies. Therefore, their consideration is integrated into the models derived. Finally, the resulting generalized versions of the Modigliani/Miller- and Miles–Ezzell-Formulas for adjusting the cost of capital to changes in leverage are applied to the situation of a corporation located in Germany after the Tax Reform Act of 2000.