Related papers: Testing Option Pricing with the Edgeworth Expansio…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for…
Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…
We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
We develop Edgeworth expansion theory for spot volatility estimator under general assumptions on the log-price process that allow for drift and leverage effect. The result is based on further estimation of skewness and kurtosis, when…
Drawing insights from the triumph of relativistic over classical mechanics when velocities approach the speed of light, we explore a similar improvement to the seminal Black-Scholes (Black and Scholes (1973)) option pricing formula by…
European options can be priced when returns follow a Student's t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student's t-distribution a Gosset approach,…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an…
We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine theorem and L\'evian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
This paper studies the model risk of the Black-Scholes (BS) model in pricing and risk-managing variable annuities motivated by its wide usage in the insurance industry. Specifically, we derive a model-free decomposition of the no-arbitrage…