We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We frst deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of...

One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This asumption can be fulfilled only in perfectly liquid markets. Since most markets are illqiud, this asumption might be too...

Since March 26, 2004, when the CBOE Futures Exchange (CFE) began trading futures written on S&P500 volatility index (VIX), volatility has become a widely accepted asset class as trading, diversifying and hedging vehicle by traders, investors and portfolio managers over the past few years. On...

An analogy based call option pricing model is put forward. The model provides a new explanation for the implied volatility skew puzzle. The analogy model is consistent with empirical findings about returns from well studied option strategies such as covered call writing and zero-beta straddles....

We propose a model for stock price dynamics that explicitly incorporates random waiting times between trades, also known as duration, and show how option prices can be alculated using this model. We use ultra-high-frequency data for blue-chip companies to motivate a particular choice of...

In this paper we recover the Black-Scholes and local volatility pricing engines in the presence of an unspecified, fully stochastic volatility. The input volatility functions are allowed to fluctuate randomly and to depend on time to expiration in a systematic way, bringing the underlying theory...

We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. A so-called volatility compensator is defined which guarantees that the Heston hybrid model with a non-zero correlation...

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is non-negative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical...

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure...

The purpose of this paper is to provide a new set of tools for policy makers at central banks. Based on the Garman-Kohlhagen formula for currency options, this research extends it with the Taylor-rule expression used for inflation targeting, thus obtaining the corresponding Call and Put options...