Annals of Finance 

About: Annals of Finance is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Mathematical finance & Portfolio. It has an ISSN identifier of 1614-2446. Over the lifetime, 410 publications have been published receiving 6358 citations.

Option pricing and Esscher transform under regime switching

Abstract: We consider the option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion (GBM). That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the underlying risky asset, depend on unobservable states of the economy which are modelled by a continuous-time Hidden Markov process. The market described by the Markov-modulated GBM model is incomplete in general and, hence, the martingale measure is not unique. We adopt a regime switching random Esscher transform to determine an equivalent martingale pricing measure. As in Miyahara [33], we can justify our pricing result by the minimal entropy martingale measure (MEMM).

A dynamic model of entrepreneurship with borrowing constraints: theory and evidence

Abstract: Does wealth beget wealth and entrepreneurship, or is entrepreneurship mainly determined by an individual’s ability? A large literature studies the relationship between wealth and entry to entrepreneurship to inform this question. This paper shows that in a dynamic model, the existence of financial constraints to the creation of businesses implies a non-monotonic relationship between wealth and entry into entrepreneurship: the probability of becoming an entrepreneur as a function of wealth is increasing for low wealth levels—as predicted by standard static models—but it is decreasing for higher wealth levels. U.S. data are used to study the qualitative and quantitative predictions of the dynamic model. The welfare costs of borrowing constraints are found to be significant, around 6% of lifetime consumption, and are mainly due to undercapitalized entrepreneurs (intensive margin), rather than to able people not starting businesses (extensive margin).

The fundamental theorem of asset pricing for continuous processes under small transaction costs

Abstract: A version of the fundamental theorem of asset pricing is proved for continuous asset prices with small proportional transaction costs. Equivalence is established between: (a) the absence of arbitrage with general strategies for arbitrarily small transaction costs \({\varepsilon > 0}\), (b) the absence of free lunches with bounded risk for arbitrarily small transaction costs \({\varepsilon > 0}\), and (c) the existence of \({\varepsilon}\)-consistent price systems—the analogue of martingale measures under transaction costs—for arbitrarily small \({\varepsilon > 0}\). The proof proceeds through an explicit construction, as opposed to the usual separation arguments. The paper concludes comparing numeraire-free and numeraire-based notions of admissibility, and the corresponding martingale and local martingale properties for consistent price systems.

Affine fractional stochastic volatility models

Abstract: By fractional integration of a square root volatility process, we propose in this paper a long memory extension of the Heston (Rev Financ Stud 6:327–343, 1993) option pricing model. Long memory in the volatility process allows us to explain some option pricing puzzles as steep volatility smiles in long term options and co-movements between implied and realized volatility. Moreover, we take advantage of the analytical tractability of affine diffusion models to clearly disentangle long term components and short term variations in the term structure of volatility smiles. In addition, we provide a recursive algorithm of discretization of fractional integrals in order to be able to implement a method of moments based estimation procedure from the high frequency observation of realized volatilities.

Relative arbitrage in volatility-stabilized markets

Abstract: We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a positive quantity that can be estimated or even computed from a given market structure, be ‘‘sufficiently large’’. We show that conditions which satisfy these criteria are manifestly present in the U.S. equity market. We then construct examples of abstract markets in which the criteria hold. These abstract markets allow us to isolate conditions similar to those prevalent in actual markets, and to construct explicit portfolios under these conditions. We study in some detail a specific example of an abstract market which is volatility-stabilized, in that the return from the market portfolio has constant drift and variance rates while the smallest stocks are assigned the largest volatilities. A rather interesting probabilistic structure emerges, in which time changes and the asymptotic theory for planar Brownian motion play crucial roles. The largest stock and the overall market grow at the same, constant rate, though individual stocks fluctuate widely.