International Journal of Theoretical and Applied Finance

We give sufficient conditions on the underlying filtration such that all totally inaccessible stopping times have compensators which are absolutely continuous. If a semimartingale, strong Markov process X has a representation as a solution of a stochastic differential equation driven by a Wiener process, Lebesgue measure, and a Poisson random measure, then all compensators of totally inaccessible stopping times are absolutely continuous with respect to the minimal filtration generated by X. However Çinlar and Jacod have shown that all semimartingale strong Markov processes, up to a change of time and slightly of space, have such a representation.

With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren–Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.

Defaults arising from illiquidity can lead to private workouts, formal bankruptcy proceedings or even liquidation. All these outcomes can result in deadweight losses. Corporate illiquidity in the presence of realistic capital market frictions can be managed by (a) equity dilution, (b) carrying positive cash balances, or (c) entering into loan commitments with a syndicate of lenders. An efficient way to manage illiquidity is to rely on mechanisms that transfer cash from "good states" into "bad states" (i.e., financial distress) without wasting liquidity in the process. In this paper, we first investigate the impact of costly equity dilution as a method to deal with illiquidity, and characterize its effects on corporate debt prices and optimal capital structure. We show that equity dilution produces lower firm value in general. Next, we consider two alternative mechanisms: cash balances and loan commitments. Abstracting from future investment opportunities and share re-purchases, which are strong reasons for corporate cash holdings, we show that carrying positive cash balances for managing illiquidity is in general inefficient relative to entering into loan commitments, since cash balances (a) may have agency costs, (b) reduce the riskiness of the firm thereby lowering the option value to default, (c) postpone or reduce dividends in good states, and (d) tend to inject liquidity in both good and bad states. Loan commitments, on the other hand, (a) reduce agency costs, and (b) permit injection of liquidity in bad states as and when needed. Then, we study the trade-offs between these alternative approaches to managing corporate illiquidity. We show that loan commitments can lead to an improvement in overall welfare and reduction in spreads on existing debt for a broad range of parameter values. We derive explicit pricing formulas for debt and equity prices. In addition, we characterize the optimal draw down strategy for loan commitments, and study its impact on optimal capital structure.

We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asymptotic expansion of the bivariate transition density in Wu (forthcoming) allows calibration of the SABR model with piecewise constant parameters and calculation of forward volatility. We then investigate empirically whether current option prices at multiple maturities contain useful information in predicting future option prices and future implied volatility. We undertake this investigation using data on options on the euro-dollar, sterling-dollar, and dollar-yen exchange rates. We find that prices across maturities do indeed have predictive value. Moreover, we find that model-based forward volatility extracts this predicative information better than a standard "model-free" measure of forward volatility and better than spot implied volatility. The enhancement to out-of-sample forecasting accuracy gained from model-based forward volatility is greatest at longer forecasting horizons.