We deal with several efficient discretization methods for the simulation of the Heston stochastic volatility model. The resulting schemes can be used to calculate all kind of options and corresponding sensitivities, in particular the exotic options that cannot be valued with closed-form solutions. We focus on to the (computational) efficiency of the simulation schemes: though the Broadie and Kaya (2006) paper provided an exact simulation method for the Heston dynamics, we argue why its practical use might be limited. Instead we consider efficient approximations of the exact scheme, which try to exploit certain distributional features of the underlying variance process. The resulting methods are fast, highly accurate and easy to implement. We conclude by numerically comparing our new schemes to the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-Jäckel scheme, the Full Truncation scheme of Lord et al. and the Quadratic Exponential scheme of Andersen.
In this paper we deal with the pricing of stock, foreign exchange and inflation options under stochastic interest rates and stochastic volatility. We consider a foreign exchange framework for the pricing inflation-indexed options in which the valuation of stock and foreign exchange options can be treated as a nested case. We assume multi-factor Gaussian rates for both the nominal (domestic) as the real (foreign) economy, which economies (currencies) can be exchanged against each other by means of the inflation index (exchange rate) which is driven by log-normal dynamics with a stochastic volatility component. Furthermore we allow for a general correlation structure between the drivers of the volatility, the inflation index, the nominal and the real rates. We derive explicit option pricing formulas for various securities, like vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. All these options can be valued in closed-form under Schöbel-Zhu (1999) stochastic volatility, whereas we device an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston (1993) model.
A quantitative analysis on the pricing of forward starting options under stochastic volatility and stochastic interest rates is performed. The main finding is that forward starting options not only depend on future smiles, but also directly on the evolution of the interest rates as well as the dependency structures among the underlying asset, the interest rates, and the stochastic volatility: compared to vanilla options, dynamic structures such as forward starting options are much more sensitive to model specifications such as volatility, interest rate, and correlation movements. We conclude that it is of crucial importance to take all these
van Haastrecht and PelsserJournal of Futures Markets DOI: 10.1002/fut factors explicitly into account for a proper valuation and risk management of these securities. The performed analysis is facilitated by deriving closed-form formulas for the valuation of forward starting options, hereby taking the stochastic volatility, stochastic interest rates as well the dependency structure between all these processes explicitly into account. The valuation framework is derived using a probabilistic approach, enabling a fast and efficient evaluation of the option price by Fourier inverting the forward starting characteristic functions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.