International Journal of Theoretical and Applied Finance

We present a nested Monte Carlo (NMC) approach implemented on graphics processing units (GPUs) to X-valuation adjustments (XVAs), where X ranges over C for credit, F for funding, M for margin, and K for capital. The overall XVA suite involves five compound layers of dependence. Higher layers are launched first, and trigger nested simulations on-the-fly whenever required in order to compute an item from a lower layer. If the user is only interested in some of the XVA components, then only the sub-tree corresponding to the most outer XVA needs be processed computationally. Inner layers only need a square root number of simulation with respect to the most outer layer. Some of the layers exhibit a smaller variance. As a result, with GPUs at least, error-controlled NMC XVA computations are doable. But, although NMC is naively suited to parallelization, a GPU implementation of NMC XVA computations requires various optimizations. This is illustrated on XVA computations involving equities, interest rate, and credit derivatives, for both bilateral and central clearing XVA metrics.

We develop a model for indifference pricing in derivatives markets, where price quotes have bid–ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor’s views, risk preferences and financial position as well as on the price quotes. Computational techniques of convex optimization allow for fast computation of the hedging portfolios and prices as well as sensitivities with respect to various model parameters. We illustrate the techniques by pricing and hedging of exotic derivatives on S&P index using call and put options, forward contracts and cash as the hedging instruments. The optimized static hedges provide good approximations of the options payouts and the spreads between indifference selling and buying prices are quite narrow as compared with the spread between superhedging and subhedging prices.

The goal of this paper is to develop a reduced-form model for pricing derivatives on the overnight rate. The model incorporates jumps around central bank (CB) meetings. More specifically, rate changes are decomposed into fluctuations between CB meetings and deterministic timed jumps following CB meetings. This approach is useful for practitioners, since it allows the extraction of expectations regarding central bank decisions embedded in liquid instruments, as well as the use of these expectations for the pricing of less liquid derivatives, such as options, in a consistent manner. We discuss applications to 30-Day Fed funds options and IDI options traded in Brazil.

We analyze variance, skewness and kurtosis risk premia and their option-implied and realized components as predictors of excess market returns and of the cross-section of stock returns. We find that the variance risk premium is the only moment-based variable to predict S&P 500 index excess returns, with a monthly out-of-sample $R^2$ above 6% for the period between 2001 and 2014. Nonetheless, all aggregate moment-based variables are effective in predicting the cross-section of stock returns. Self-financed portfolios long on the stocks least exposed to the aggregate moment-based variable and short on the stocks most exposed to it achieve positive and significant Carhart 4-factor alphas and a considerably higher Sharpe ratio than the S&P 500 index, with positive skewness.

Banking system crises are complex events that in a short span of time can inflict extensive damage to banks themselves and to the external economy. The crisis literature has so far identified a number of distinct effects or channels that can propagate distress contagiously both directly within the banking network itself and indirectly, between the network and the external economy. These contagious effects, and the potential events that trigger these effects, can explain most aspects of past crises, and are thought to be likely to dominate future financial crises. Since the current international financial regulatory regime based on the Basel III Accord does a good job of ensuring that banks are resilient to such contagion effects taken one at a time, systemic risk theorists increasingly understand that future crises are likely to be dominated by the spillovers between distinct contagion channels. The present paper aims to provide a model for systemic risk that is comprehensive enough to include the important contagion channels identified in the literature. In such a model one can hope to understand the dangerous spillover effects that are expected to dominate future crises. To rein in the number and complexity of the modelling assumptions, two requirements are imposed, neither of which is yet well-known or established in the main stream of systemic risk research. The first, called stock-flow consistency, demands that the financial system follows a rigorous set of rules based on accounting principles. The second requirement, called asset-liability symmetry, implies that every proposed contagion channel has a dual channel obtained by interchanging assets and liabilities, and that these dual channel pairs have a symmetric mathematical representation.

This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are heterogeneous in risk-preferences.