The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for...

The hedging argument of Black and Scholes (1973) hinges on the assumption that a continuously rebalanced asset portfolio satisfies the continuous-time self-financing condition. This condition, which is a special case of the continuous-time budget equation of Merton (1971), is believed to...

The market for ultra short-term (zero days-to-expiry or 0DTE) options has grown exponentially over the last few years. In 2023, daily volume in 0DTEs reached over 45% of overall daily options volume. After briefly describing this exploding new market, we present a novel pricing formula designed...

A number of studies on the S&P 500 index options market claim that the no arbitrage assumption cannot be rejected for this market because either the martingale restriction defined in Longstaff (1995) cannot be rejected by the data, or, even when it is rejected, a large proportion of the...

Although the effect of interest rate stochasticity can safely be ignored for short-dated exchange traded volatility derivatives, this is not the case for the kind of long-dated OTC derivatives often used by insurance companies and other financial institutions. We therefore extend existing...

Sellers of variance swaps earn time-varying risk premia for their exposure to realized variance, the level of variance swap rates, and the slope of the variance swap curve. To measure risk premia, we estimate a dynamic term structure model that decomposes variance swap rates into expected...

This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions...

Recently, simulation methods combined with regression techniques have gained importance when it comes to American option pricing. In this paper we consider such methods and we examine numerically their convergence properties. We first consider the Least Squares Monte-Carlo (LSM) method of...

This paper investigates the effect of uncertainty about input parameters on the accuracy of real option valuation. It compares the error from no-arbitrage valuation with the error from using DCF. Despite the theoretical superiority of no-arbitrage valuation it is shown to be less accurate than...

The prices of derivatives contracts can be used to estimate ‘risk-neutral' probability density functions that give an indication of the weight investors place on different future prices of their underlying assets, were they risk-neutral. In the likely case that investors are risk-averse, this...