We study zero-sum optimal stopping games associated with perpetual convertible bonds in an extension of the Black-Merton-Scholes model random dividends under various information flows. In this...

The Black-Scholes (1973) option pricing model is used to value a wide range of option contracts. However, the model often inconsistently prices deep in-themoney and deep out-of-the-money options. Options’ professionals refer to this phenomenon as a volatility ‘skew’ or ‘smile.’ In this paper, we apply an extension of the Black-Scholes model developed by Jarrow and Rudd (1982) to an investigatio...

Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black-Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrödinger equation. The nonlinear approach comes in two flavors: for the case of constant volat...

We derive error estimates for multinomial approximations of American options in a multidimensional jump–diffusion Merton’s model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type of approximations were not obtained before. Our main tool is the strong approximations theorems for i.i.d. random vectors which were obtained in [14]. For th...

The need of considering price dynamics alternative to the classical Black-Scholes model for derivatives pricing is widely known. The stochastic variability of market parameters and in particular the empirical evidence of non constant surfaces of implied volatility in real markets require more realistic models for the assets dynamics. Many approaches are available to obtain a better fitting of m...

This paper presents an empirical test of Dupire's (1993) option price inversion approach using FT–SE 100 index options. The performance of option deltas determined using the Dupire approach is compared to the performance of a pair of Black-Scholes (1973) based deltas. The study finds that Black-Scholes based deltas out-perform the Dupire-deltas, which is consistent with the results in synthesiz...

This study applies fuzzy set theory to the vulnerable Black-Scholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value Black-Scholes options subject to non-identical rationality and correlated credit risk. Although no analytica...

Following an approach introduced by Lagnado and Osher (1997), we study Tikhonov regularization applied to an inverse problem important in mathematical finance, that of calibrating, in a generalized Black–Scholes model, a local volatility function from observed vanilla option prices. We first establish W 1,2 p estimates for the Black–Scholes and Dupire equations with measurable ingredients. Appl...

We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach pred...

We recover the properties of a wide class of far from extremal charged black branes from properties of near extremal black branes, generalizing the results of Danielsson, Guijosa and Kruczenski.