THE AFFINE RATIONAL POTENTIAL MODEL

We develop a class of rational term structure models in the framework of the potential approach based upon a family of positive supermartingales that are driven by an affine Markov process. These models generally feature nonnegative interest rates and analytic pricing formulae for zero bonds, caps, swaptions, and European currency options, even in the presence of multiple factors. Moreover, in a model specification, the short rate stays near the zero lower bound for an extended period.

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation

We consider stochastic differential equations driven by a general Lévy processes (SDEs) with infinite activity and the related, via the Feynman–Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solution of PIDE using a numerical method for the SDEs. The method is based on three ingredients: (1) we approximate small jumps by a diffusion; (2) we use restricted jump-adaptive time-stepping; and (3) between the jumps we exploit a weak Euler approximation. We prove weak convergence of the considered algorithm and present an in-depth analysis of how its error and computational cost depend on the jump activity level. Results of some numerical experiments, including pricing of barrier basket currency options, are presented.

An Open Innovation Intraday Implied Volatility for Pricing Australian Dollar Options

This study introduces the intraday implied volatility (IV) for pricing the Australian dollar (AUD) options. The IV is estimated using the at-the-money one-month, two-month, and three-month maturity AUD options traded in the opening, midday, and closing period of a trading day. The Mincer-Zarnowitz regression test evaluates the predictive power of IV to forecast the foreign exchange volatility for the within-week, one-week, and one-month horizon. The mean absolute error, mean squared error, and root mean squared error measures are employed to assess the performance of IV in estimating the price of currency options for the within-week, one-week, and one-month horizon. This study reveals four critical findings. First, a three-month maturity IV does not contain vital information for pricing options. Second, IV incorporated information is not relevant to compute the value of options for a horizon of less than a week. Third, IV in the closing period of Monday or Tuesday subsumes most of the essential information to estimate options price. Fourth, the shorter (longer) maturity IV provides critical information to price options for the shorter (longer) horizon. The intraday IV is a new dimension of unobservable volatility in accurately pricing currency options for researchers and practitioners.

Arbitrage Bounds on Currency Basket Options

This article exploits arbitrage valuation bounds on currency basket options. Instead of using a sophisticated model to price these options, we consider a set of pricing models that are consistent with the prices of available hedging assets. In the absence of arbitrage, we identify valuation bounds on currency basket options without model specifications. Our results extend the work in the literature by seeking tight arbitrage valuation bounds on these options. Specifically, the valuation bounds are enforced by static portfolios that consist of both cross-currency options and individual options denominated in the numeraire currency.