This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

This paper studies modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in...

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitztype conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean,...

We propose a model that explains the build-up of short term debt when the creditors are strategic and have different beliefs about the prospects of the borrowers' fundamentals. We define a dynamic game among creditors, whose outcome is the short term debt process as a function of the borrower's...

We analyze debt issuance in the continuous time limit and when the issuer's asset is subject to downward jump risk. We find the debt capacity in equilibrium and an illiquidity barrier. When the asset-to-debt ratio is above the barrier the issuer is liquid, whereas below the barrier it can no...

This paper explores, in a multi-period setting, the funding liquidity of a borrower that finances its operations through short term debt. The short term debt is provided by a continuum of agents with heterogeneous beliefs about the prospects of the borrower. In each period, creditors observe the...