Related papers: Three little arbitrage theorems
We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The…
We show that the Axiom of Real Determinacy $\mathsf{AD}_{\mathbb{R}}$ and the Axiom of Real Blackwell Determinacy $\mathsf{Bl}\text{-}\mathsf{AD}_{\mathbb{R}}$ are equivalent in $\mathsf{ZF}$+$\mathsf{DC}$. This answers the question of…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices…
We study $N$-player optimal execution games in an Obizhaeva--Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
We have obtained charged asymptotically AdS black hole solutions in Einstein Gauss Bonnet gravity in presence of string cloud. It turns out that there exist three black holes in certain range of parameters for small enough chemical…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
We study the binomial, trinomial, and Black-Scholes-Merton models of option pricing. We present fast parallel discrete-time finite-difference algorithms for American call option pricing under the binomial and trinomial models and American…
By consideration of a Einstein-dilaton non-linear charged gravitating system, it has been shown that this theory is confronted with the problem of indeterminacy. It means that the number of independent differential equations is one less…
We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction…
ATSM are widely applied for pricing of bonds and interest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open question. First, the standard approach to ATSM uses the…
In this paper, we study the multi-asset Black-Scholes model in terms of the importance that the correlation parameter space (equivalent to an $N$ dimensional hypercube) has in the solution of the pricing problem. We show that inside of this…
This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta…
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…
In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric…
The bubble is a controversial and important issue. Many methods which based on the rational expectation have been proposed to detect the bubble. However, for some developing countries, epically China, the asset markets are so young that for…
We analyze a generalized version of the Black-Scholes equation depending on a parameter $a\!\in \!(-\infty,0)$. It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case $a\nearrow 0$. We show…
We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes…
In the framework of the Einstein-Maxwell-aether theory, we present two new classes of exact charged black hole solutions, which are asymptotically flat and possess the universal as well as Killing horizons. We also construct the Smarr…
A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends on the value of the return. The solution…