arXiv research

Analytical tools for pricing power options in Lévy models.

We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of $V=(S^α_T-K)^{+}$ and $V=(S^α_T-K^α)^{+}$ ($α>0$)respectively. Using quadratic Taylor approximations, We develop the computing formula of implied volatility in European power call op…

The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…

Paper introduces a model to capture power option volatility.

In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…

Develops European power option pricing under correlated interest rate and asset processes.

Reliability Options are capacity remuneration mechanisms aimed at enhancing security of supply in electricity systems. They can be framed as call options on electricity sold by power producers to System Operators. This paper provides a comprehensive mathematical treatment of Reliability Options. Their value is first de…

\begin{abstract} The aim of this paper is to study the spanning power of options in a static financial market that allows non-integrable assets. Our findings extend and unify the results in [8,9,18] for $L_p$-models. We also apply the spanning power properties to the pricing problem. In particular, we show that prices …

Paper solves multi-dimensional passport option pricing problem using machine learning.

The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.

Study proves duality in exotic option pricing under uncertain model and delayed information.

Paper proposes methods for pricing FX-linked Bermudan options using quantization.

In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our numerical results show that a second order expansion provides accurate prices o…

The paper models cryptocurrency price and volatility with jumps and fractional volatility.

It is well known that any sufficiently regular one-dimensional payoff function has an explicit static hedge by bonds, forward contracts and lots of vanilla options. We show that the natural extension of the corresponding representation leads to a static hedge based on the same instruments along with traffic light optio…

MNN improves American call option pricing accuracy.

Closed-form pricing method for multi-asset options.

This paper compares machine learning models for pricing European options.

We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a model-independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence…

In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset…

The paper provides approximations for pricing Asian options using a mixed fractional Brownian motion with jumps.

This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…

We build a methodology that takes a given option price in the tails with strike $K$ and extends (for calls, all strikes > $K$, for puts all strikes $< K$) assuming the continuation falls into what we define as "Karamata Constant" over which the strong Pareto law holds. The heuristic produces relative prices for options…

Enhanced volatility forecasting using options data and rough volatility model.

We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the possibility of default and correlation between different assets. We show how to…

The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative Lévy process ξwith unbounded variation. We also derive a Geman-Yor type formula for Asian options prices in a financial marke…

Framework optimizes PV-battery investment timing to maximize value.

We develop series expansions in powers of $q^{-1}$ and $q^{-1/2}$ of solutions of the equation $ψ(z) = q$, where $ψ(z)$ is the Laplace exponent of a hyperexponential Lévy process. As a direct consequence we derive analytic expressions for the prices of European call and put options and their Greeks (Theta, Delta, and G…

Critical volatility triggers log-normal to power-law transitions in interconnected systems.

The paper uses the variance-gamma model to price options and explain excess kurtosis.

The paper derives formulas for option pricing and random walk expectations.

Efficiently values and computes sensitivities of Bermudan options using Method of Lines.

The article prices exchange options using variance gamma-like models.

The paper analyzes binary option markets with exogenous information and price sensitivity.

The paper solves European option pricing under Heston model using artificial boundary method.

Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…

One popular approach to option pricing in Lévy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). As in practice large classes of models are maintained simultaneous…

Model predicts jump risk premia influencing cryptocurrency futures and option performance.

We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter [2004], where the supply function $S^ε(s,ν)$ depends on a parameter $ε\geq 0$ with $S^0(s,ν)=s$ corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [2010] of the super-hedging cost of a…

New method uses tensor networks to price multi-asset options efficiently.

Paper presents a new computational technique for finance using ERM and neural networks.

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 type. An option pricing formula is derived from the same superposition of Black…

High performance computing (HPC) is a very attractive and relatively new area of research, which gives promising results in many applications. In this paper HPC is used for pricing of American options. Although the American options are very significant in computational finance; their valuation is very challenging, espe…

Quantum computing improves Monte Carlo option pricing for complex derivatives.

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimart…

In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning on the remaining underlying assets and calculating the mixed exponential-power mo…

Enhances option pricing for American-style options using JDOI method.

Study finds rough volatility models underperform in SPX option pricing.