We propose a modification of the option pricing framework derived by Borland which removes the possibilities for arbitrage within this framework. It turns out that such arbitrage possibilities arise due to an incorrect derivation of the martingale transformation in the non-Gaussian option models...

We model the volatility of a single risky asset using a multifactor (matrix) Wishart affine process, recently introduced in finance by Gourieroux and Sufana. As in standard Duffie and Kan affine models the pricing problem can be solved through the Fast Fourier Transform of Carr and Madan. A...

The present paper addresses the problem of computing implied volatilities of options written on a domestic asset based on implied volatilities of options on the same asset expressed in a foreign currency and the exchange rate. It proposes an original method together with explicit formulae to...

We report on the adequacy of using Sato processes to value equity structured products. In models used to price options on realized variance, the latter must be a random variable with a positive variance. An analysis of this variance of realized variance for Sato processes shows that these...

We introduce a simple model for the pricing of European-style options when the underlying dividend process is given by a geometric Brownian motion with Markov-modulated coefficients. It turns out that the corresponding stock process is characterized by both stochastic coefficients and jumps....

Estimating the volatility from the underlying asset price history for the discrete observations case is a challenging inference problem. Yet it has attracted much research interest due to the key role of volatility in many areas of finance. In this paper we consider the Heston stochastic...

Many empirical researches report that value-at-risk (VaR) measures understate the actual 1% quantile, while for Inui, K., Kijima, M. and Kitano, A., VaR is subject to a significant positive bias. Stat. Probab. Lett., 2005, 72, 299-311. proved that VaR measures overstate significantly when...

In this paper we study a correlation-based LIBOR market model with a square-root volatility process. This model captures downward volatility skews through taking negative correlations between forward rates and the multiplier. An approximate pricing formula is developed for swaptions, and the...

We present a new and general technique for obtaining closed-form expansions for prices of options in the Heston model, in terms of Black-Scholes prices and Black-Scholes Greeks up to arbitrary order. We then apply the technique to solve, in detail, the cases for the second-order and third-order...

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment s+ can be obtained by solving (numerically) a simple equation. This yields a leading-order expansion for the implied volatility at large strikes: σBS(k, T)2T ∼ Ψ(s+ - 1) × k (Roger...