Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options
This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX options, and vice ...
Portfolio Benchmarking Under Drawdown Constraint and Stochastic Sharpe Ratio
We consider an investor who seeks to maximize her expected utility of wealth relative to a benchmark, or target over a finite time horizon, and under a portfolio drawdown constraint, in a market with local stochastic volatility. We propose a new investor ...
Variational Analysis for Options with Stochastic Volatility and Multiple Factors
This paper performs a variational analysis for a class of European or American options with stochastic volatility models, including those of Heston and of Achdou and Tchou. Taking into account partial correlations and the presence of multiple factors, we ...
Option Pricing in a One-Dimensional Affine Term Structure Model via Spectral Representations
Under a mild condition on the branching mechanism, we provide an eigenvalue expansion for the pricing semigroup in a one-dimensional positive affine term structure model. This representation, which is based on results from Ogura [Publ. Res. Inst. Math. ...
Regression-Based Complexity Reduction of the Nested Monte Carlo Methods
In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has an especially simple form for time discretized diffusion processes. We analyze ...
Time-Coherent Risk Measures for Continuous-Time Markov Chains
We propose an approach to risk evaluation of cost processes in continuous-time Markov chains. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a concept of time coherence as ...
Dirichlet Forms and Finite Element Methods for the SABR Model
We propose a deterministic numerical method for pricing vanilla options under the SABR stochastic volatility model, based on a finite element discretization of the Kolmogorov pricing equations via nonsymmetric Dirichlet forms. Our pricing method is valid ...
Asymptotic Approximation of Optimal Portfolio for Small Time Horizons
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton--Jacobi--Bellman partial differential equation (HJB PDE), we obtain a closed-form formula for a ...
Principal-Agent Problem with Common Agency Without Communication
In this paper, we consider a problem of contract theory in which several Principals hire a common Agent and we study the model in the continuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we reduce the ...
Liquidity Induced Asset Bubbles via Flows of ELMMs
We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in [R. Jarrow, P. Protter, and A. Roch, Quant. ...
Local Volatility, Conditioned Diffusions, and Varadhan's Formula
We study classes of stochastic volatility models and derive asymptotic formulae for the associated local volatility surface. This gives new insight into the geometry of a reasonable local volatility surface, especially in extreme moneyness regimes. ...