In this paper we give an alternative proof of the convexity of the implied volatility curve as a function of the strike, for stochastic volatility models in the uncorrelated case. Our method is based on the computation of the corresponding first and second derivatives, and on Malliavin calculus...

A Margrabe or exchange option is an option to exchange one asset for another. In a general stochastic volatility framework, by taking the second asset as a numeraire, we derive pricing as well as second order approximative pricing formulae for Margrabe options. This can only be done under...

Using a suitable Hull and White type formula we develop a methodology to obtain a second order approximation to the implied volatility for very short maturities. Using this approximation we accurately calibrate the full set of parameters of the Heston model. One of the reasons that makes our...

We present a method to develop simple option pricing approximation formulas for a fractional Heston model, where the volatility process is defined by means of a fractional integration of a diffusion process. This model preserves the short-time behaviour of the Heston model, at the same time it...

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull...

In this paper we propose a general technique to develop first and second order closed-form approximation formulas for short-time options with random strikes. Our method is based on Malliavin calculus techniques and allows us to obtain simple closed-form approximation formulas depending on the...

In this paper locally risk-minimizing hedge strategies for European-style contingent claims are derived and tested for a general class of stochastic volatility models. These strategies are as easy to implement as ordinary delta hedges, yet in realistic settings they produce markedly lower hedge...

This paper derives an analytic expression for the distribution of the average volatility ds in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such an analytic form exists. Our findings...

In this paper we establish the existence and uniqueness of a solution for stochastic Volterra equations assuming that the coefficients F(t,s,x) and Gi(t,s,x) are Ft-measurable, for s[less-than-or-equals, slant]t, where {Ft} denotes the filtration generated by the driving Brownian motion. We...