Related papers: Perturbation Expansion for Option Pricing with Sto…
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a…
A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends on the value of the return. The solution…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. The formulae are obtained by using a…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a…
The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the…
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that…
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…