Natalia A. Beliaeva

A Simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model

Lattice models are workhorses of practical option pricing, especially for American options, but an important design criterion is that they need to be set up so that the interior branches recombine, otherwise, they become computationally intractable; the underlying state variable becomes path-dependent, the tree “splinters,” and the number of distinct nodes goes up exponentially rather than arithmetically as the number of time steps grows. Unfortunately, we have accumulated a great deal of evidence that volatility is time varying, which is a factor that splinters the tree. In this article, Beliaeva and Nawalkha show how to get around the problem by transforming the returns process to create two uncorrelated path-independent trees for returns and variance that can be put together into a single recombining two-dimensional lattice. The procedure is general; here they illustrate its use with the popular Heston model.

Pricing American Interest Rate Options under the Jump-Extended Vasicek Model

This paper shows how to price American interest rate options under the exponential jumps-extended Vasicek model. We modify the Gaussian jump-diffusion tree of Amin [1993] and apply to the exponential jumps-based short rate process under the Vasicek-EJ model. The tree is truncated at both ends to allow fast computation of option prices. We also consider the time-inhomogeneous version of this model, denoted as the Vasicek-EJ++ model that allows exact calibration to the initially observable bond prices. Our simulations show fast convergence of European option prices obtained using the jump-diffusion tree, to those obtained using the Fourier inversion method and the cumulant expansion method.

Transform Analysis for Pricing American Options Under Low-Dimensional Stochastic Volatility Models

This paper presents a new transform-based approach for path-independent lattice construction for pricing American options under low-dimensional stochastic volatility models. We derive multidimensional transforms which allow us to construct efficient path-independent lattices for virtually all low-dimensional stochastic volatility models given in the literature including one volatility factor-based stochastic volatility (SV) models, two volatility factors-based SV models, stochastic volatility jump (SVJ) models with one and two jump factors in the asset returns, and SVJ models with jumps in both asset returns and volatility. The lattice-based approximations of the prices of European options converge rapidly to their true prices obtained using quasi-analytical solutions.

Implicit Government Guarantee and the CDS Spreads

It is commonly agreed that the government is more likely to step in and rescue some troubled companies labeled as “too big to fail” or “too interconnected to fail.” Since there is no formal contract between these companies and the government, this potential intervention is referred to as an implicit government guarantee. We propose a new approach of assessing and estimating the implicit government guarantee and analyze whether it is reflected in the CDS spreads. We define the implicit government guarantee for a given company as the probability that the government will bail it out in case of a default. Although the company’s size affects the likelihood of government intervention, we find that financial industry membership is a more important factor. Furthermore, we find that the implicit government guarantee is priced into the CDS spreads. The government guarantee for large companies reduces the CDS spread by 16.11 bps and for small companies only by 3.73 bps. Similarly, for the financial industry, we find that the government guarantee reduces the CDS spread by 76.29 bps and for the nonfinancial industry only by 7.50 bps.