Related papers: Static replications with traffic light options
In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower c\`adl\`ag obstacle. We…
We predict that stable mobile spatio-temporal solitons can exist in arrays of periodically curved optical waveguides. We find two-dimensional light bullets in one-dimensional arrays with harmonic waveguide bending and three-dimensional…
We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…
Martingale Optimal Transport (MOT) provides a framework for robust pricing and hedging of illiquid derivatives. Classical MOT enforces exact calibration of model marginals to the mid-prices of vanilla options. Motivated by the industry…
Acyclic preferences recently appeared as an elegant way to model many distributed systems. An acyclic instance admits a unique stable configuration, which can reveal the performance of the system. In this paper, we give the statistical…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…
We regard options on VIX and Realised Variance as solutions to path-dependent partial differential equations (PDEs) in a continuous stochastic volatility model. The modeling assumption specifies that the instantaneous variance is a $C^3$…
We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not…
Straddle Option is a financial trading tool that explores volatility premiums in high-volatility markets without predicting price direction. Although deep reinforcement learning has emerged as a powerful approach to trading automation in…
I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with Student-t…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
We study superreplication of European contingent claims in discrete time in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce a suitable notion of efficient friction in this framework,…
We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there…
In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
It is known that inhomogeneous second-order macroscopic traffic models can reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic condition is violated, uniform traffic flow is unstable, and small perturbations grow…
We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…