Using the joint characteristic function of equity price and state variables, we can price contingent claims on both equity and VIX consistently. Based on linear approximation of jump size, we show that one factor models implies all VIX future contract of different maturities are perfectly...

A State Price Density (SPD) is the density function of a risk neutral equivalent martingale measure for option pricing, and is indispensible for exotic option pricing and portfolio risk management. Many approaches have been proposed in the last two decades to calibrate a SPD using financial...

Investment behaviour, techniques and choices have evolved in the options markets since the launch of options trading in 1973. Today, we are entering the field of Big Data and the explosion of information, which has become the main feature of science, impacts investors' decisions and their...

Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump-diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and...

Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as "volatility smile". They provide a discrete...

The behavior of the implied volatility surface for European options was analyzed in details in [Zumbach and Fernandez, 2011] for prices computed with a new option pricing scheme based on the construction of the risk-neutral measure for realistic processes with a finite time increment. The...

This paper presents a joint analysis of the term structure of credit default swap (CDS) spreads and the implied volatility surface. The rapid development of the CDS market has provided convenient products to extract credit risk, and its interaction with equity volatility has been analyzed in...