Review of Derivatives Research最新文献

The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Lévy processes. First, market data is calibrated to stochastic volatility inspired-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an stochastic volatility with correlated jumps model, a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta-Gamma, Delta-Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.

This paper proposes a multidimensional Hilbert transform approach for pricing discretely monitored multi-asset barrier options and computing joint survival probability in multivariate exponential Lévy asset price models. We generalize the univariate Hilbert transform method of Feng and Linetsky (Math Financ 18(3), 337–384, 2008) for single-asset barrier options and the well-known Sinc approximation theory of Stenger (Numerical methods based on sinc and analytic functions. Springer, New York, 1993) for computing the one-dimensional Hilbert transform to any dimension. We prove that, for Lévy processes with joint characteristic functions having an exponentially decaying tail, the error of our method decays exponentially in some power of the number of terms used in the expansion for each dimension. Numerical experiments demonstrate the efficiency of our method in the two-dimensional and three-dimensional problems for some popular multivariate Lévy models.

The calibration of financial models is laborious, time-consuming and expensive, and needs to be performed frequently by financial institutions. Recently, the application of artificial neural networks (ANNs) for model calibration has gained interest. This paper provides the first comprehensive empirical study on the application of ANNs for calibration based on observed market data. We benchmark the performance of the ANN approach against a real-life calibration framework that is in action at a large financial institution. The ANN based calibration framework shows competitive calibration results, roughly four times faster with less computational efforts. Besides speed and efficiency, the resulting model parameters are found to be more stable over time, enabling more reliable risk reports and business decisions. Furthermore, the calibration framework involves multiple validation steps to counteract regulatory concerns regarding its practical application.

This paper addresses arbitrage-free FX smile construction from near-term implied volatility dynamics proposed by Carr (J Financ Econ, 120(1), 1-20, 2016). The approach is directly applicable to FX option market conventions. Prices of market benchmark contracts (risk reversals and butterflies) are identified as the roots of a cubic polynomial and ATM-volatility can be matched by construction. Implied volatilities are computed with respect to (non-premium adjusted) option deltas. The approach is compared to the Vanna Volga Approach, which does not guarantee arbitrage-free prices. An empirical application to a normal and a stress scenario demonstrates that arbitrage-free implied volatilities coincide with those from the Vanna Volga Approach when prices are interpolated between the $\Delta$ 25-call and $\Delta$ 25-put options. Differences are observed when implied volatilities are extrapolated to the wings. Empirically, these differences are particularly relevant in a stress scenario during the Coronavirus crises (2020).