arXiv subjects

Robert Jarrow

Publications and source records attributed to Robert Jarrow.

8 recordsLinked to original sources

arXiv2026

Option Pricing with Time-Changed Fractional Brownian Motion: A Fractional Variance Gamma Model

Fractional Brownian motion (fBm) exhibits attractive features for financial modeling, including long-range dependence, path roughness, and anomalous diffusion. However, its non-semimartingale nature precludes the use of conventional no-arbitrage approaches to option pricing. We address this limitation by introducing a time-changed fBm, obtained by evaluating fBm at stochastic gamma activity time, where activity time represents cumulative executed trading time. The resulting process retains the defining properties of fBm while recovering the semimartingale structure. Building on this construction, we develop the fractional Variance Gamma (fVG) model and propose a generalized method of moments (GMM) estimation procedure for option pricing. An empirical analysis of the S\&P 500 yields an estimated Hurst exponent of approximately 0.45, consistent with mildly sublinear temporal scaling of return moments.

q-fin.MF↗

arXiv2025

Differential Beliefs in Financial Markets Under Information Constraints: A Modeling Perspective

We apply the theory of McKean-Vlasov-type SDEs to study several problems related to market efficiency in the context of partial information and partially observable financial markets: (i) convergence of reduced-information market price processes to the true price process under an increasing information flow; (ii) a specific mechanism of shrinking biases under increasing information flows; (iii) optimal aggregation of expert opinions by a trader seeking a positive alpha. All these problems are studied by means of (conditional) McKean-Vlasov-type SDEs, Wasserstein barycenters, KL divergence and relevant tools from convex optimization, optimal control and nonlinear filtering. We supply the theoretical results in (i)-(iii) with concrete simulations demonstrating how the proposed models can be applied in practice to model financial markets under information constraints and the arbitrage-seeking behavior of traders with differential beliefs.

q-fin.MF↗

arXiv2023

Filtration Reduction and Completeness in Jump-Diffusion Models

This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted to the original economy using the notion of consistency. For pedagogical purposes, we begin with simple setups and progressively extend to models of increasing generality.

q-fin.MF↗

arXiv2021

Computing the Probability of a Financial Market Failure: A New Measure of Systemic Risk

This paper characterizes the probability of a market failure defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. The characterization employs a multivariate Cox process across the G-SIBs, which allows us to relate our work to the existing literature on intensity-based models. Various theorems related to market failure probabilities are derived, including the probability of a market failure due to two banks defaulting over the next infinitesimal interval, the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to 1.

q-fin.MF↗

arXiv2011

Is there a bubble in LinkedIn's stock price?

Recent academic work has developed a method to determine, in real time, if a given stock is exhibiting a price bubble. Currently there is speculation in the financial press concerning the existence of a price bubble in the aftermath of the recent IPO of LinkedIn. We analyze stock price tick data from the short lifetime of this stock through May 24, 2011, and we find that LinkedIn has a price bubble.

q-fin.RM↗

arXiv2011

Discretely sampled variance and volatility swaps versus their continuous approximations

Discretely sampled variance and volatility swaps trade actively in OTC markets. To price these swaps, the continuously sampled approximation is often used to simplify the computations. The purpose of this paper is to study the conditions under which this approximation is valid. Our first set of theorems characterize the conditions under which the discretely sampled swap values are finite, given the values of the continuous approximations exist. Surprisingly, for some otherwise reasonable price processes, the discretely sampled swap prices do not exist, thereby invalidating the approximation. Examples are provided. Assuming further that both swap values exist, we study sufficient conditions under which the discretely sampled values converge to their continuous counterparts. Because of its popularity in the literature, we apply our theorems to the 3/2 stochastic volatility model. Although we can show finiteness of all swap values, we can prove convergence of the approximation only for some parameter values.

math.PR↗

arXiv2009

Housing Market Microstructure

In this article, we develop a model for the evolution of real estate prices. A wide range of inputs, including stochastic interest rates and changing demands for the asset, are considered. Maximizing their expected utility, home owners make optimal sale decisions given these changing market conditions. Using these optimal sale decisions, we simulate the implied evolution of housing prices providing insights into the recent subprime lending crisis.

q-fin.TR↗

arXiv2004

Modeling Credit Risk with Partial Information

This paper provides an alternative approach to Duffie and Lando [Econometrica 69 (2001) 633-664] for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by constructing an economy where the market sees the manager's information set plus noise. The noise makes default a surprise to the market. In contrast, we obtain a reduced form model by constructing an economy where the market sees a reduction of the manager's information set. The reduced information makes default a surprise to the market. We provide an explicit formula for the default intensity based on an Azema martingale, and we use excursion theory of Brownian motions to price risky debt.

math.PR↗