SINH-ACCELERATION: EFFICIENT EVALUATION OF PROBABILITY DISTRIBUTIONS, OPTION PRICING, AND MONTE CARLO SIMULATIONS

Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around [Formula: see text]. The Fourier transform techniques reduce calculation of probability distributions and option prices in the evaluation of integrals whose integrands are analytic in domains enjoying these properties. In the paper, we suggest to use changes of variables of the form [Formula: see text] and the simplified trapezoid rule to evaluate the integrals accurately and fast. We formulate the general scheme, and apply the scheme for calculation probability distributions and pricing European options in Lévy models, the Heston model, the CIR model, and a Lévy model with the CIR-subordinator. We outline applications to fast and accurate calibration procedures and Monte Carlo simulations in Lévy models, regime switching Lévy models that can account for stochastic drift, volatility and skewness, the Heston model, other affine models and quadratic term structure models. For calculation of quantiles in the tails using the Newton or bisection method, it suffices to precalculate several hundreds of values of the characteristic exponent at points on an appropriate grid (conformal principal components) and use these values in formulas for cpdf and pdf.

A Shadow Rate or a Quadratic Policy Rule? The Best Way to Enforce the Zero Lower Bound in the United States

We study whether it is better to enforce the zero lower bound (ZLB) in models of U.S. Treasury yields using a shadow rate model or a quadratic term structure model. We show that the models achieve a similar in-sample fit and perform comparably in matching conditional expectations of future yields. However, when the recent ZLB period is included in the sample, the models’ ability to match conditional expectations away from the ZLB deteriorates because the time-series dynamics of the pricing factors change. In addition, neither model provides a reasonable description of conditional volatilities when yields are away from the ZLB.

Stochastic volatility asymptotics of defaultable interest rate derivatives under a quadratic Gaussian model

Stochastic volatility of underlying assets has been shown to affect significantly the price of many financial derivatives. In particular, a fast mean-reverting factor of the stochastic volatility plays a major role in the pricing of options. This paper deals with the interest rate model dependence of the stochastic volatility impact on defaultable interest rate derivatives. We obtain an asymptotic formula of the price of defaultable bonds and bond options based on a quadratic term structure model and investigate the stochastic volatility and default risk effects and compare the results with those of the Vasicek model.