This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging of a large investor. Our main...

We present a unified, market-complete model that integrates both Bachelier and Black- Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that experiences the possibility of negative security prices or...

Slightly over fifty years ago, the Black-Scholes option pricing model revolutionized investing by enabling a shift from linear to non-linear payoff structures. Myron Scholes later published two papers documenting the performance of passive option strategies that outperformed the underlying index...

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis...

The frequency and economic damage of natural disasters have increased globally over the last two decades due to climate change. This increase has an impact on the disaster insurance field, particularly in the calculation of premiums. Many regions have a shortcoming in employing insurance because...

The concern of this article is to derive a regime switching model that can be utilized to price European call options for a financial market that exhibits structural changes with time. The model is formulated based on the fact that the underlying asset process is described by a geometric...

The publication of the Black-Scholes formula in 1973 appeared for the first time to put the pricing of financial options onto a rational and objective basis. While earlier option-pricing models relied on a subjective estimate of the stock’s uncertain future growth rate, the Black-Scholes model...

The small-maturity implied volatility of an asset pricing model is fully determined by the asymptotics of traded option prices, and thus model-free expressions are available. We show how by sharpening one such expression it is possible to derive a general formula for the leading order of the...

Numerical methods such as binomial and finite difference methods can be used to price options however the problem is when the options have early exercise features. In this research project, we investigate the effectiveness and accuracy of Monte Carlo methods in pricing American options. We...

We present a mixture of normalizing flows (MoNF) approach to European option pricing with guarantees that its estimations are free from static arbitrage. In contrast to many existing methods that meet economic rationality constraints (e.g., non-arbitrage) by introducing auxiliary losses, our...

We seek to estimate a portfolio of option prices in an entirely data driven way, at any future time, for trading and risk management purposes in a model independent way. We do not know the model driving the dynamics of the actual stock prices, but only observe discretely their evolution in the...

This research article provides criticism and arguments why the canonical framework for derivatives pricing is incomplete and why the delta-hedging approach is not appropriate. An argument is put forward, based on the efficient market hypothesis, why a proper risk-adjusted discount rate should...

This article explores the quantitative and qualitative dimensions of volatility and their implications for cultural analysis in a range of fields. From quantitative finance, it takes the notion of 'delta-hedging', the suspension or neutralization of directionality to get access to volatility,...

The concern of this article is to derive a regime switching model that can be utilized to price European call options for a financial market that exhibits structural changes with time. The model is formulated based on the fact that the underlying asset process is described by a geometric...

We present a computationally tractable method for simulating arbitrage free implied volatility surfaces. We illustrate how our method may be combined with a factor model for the implied volatility surface to generate dynamic scenarios for arbitrage-free implied volatility surfaces. Our approach...

This paper develops a dynamic joint model of the implied volatility (IV) surface and its underlying asset, impervious to arbitrage and quick to estimate. It combines an asymptotically well-behaved, parametric IV surface representation with a two-component variance, and non-Gaussian asymmetric...

In recent years fractional partial differential equations and their solutions through analytical methods is a dynamic and imperative research area. In this context finding the exact solution of fractional partial differential equations by employing variant tactics has been the pivotal region of...

We overcome the key limitations of the Black-Scholes model. In doing so, we provide an explicit, simple price formula for the European option that is identical to the classical Black-Scholes formula. Moreover, we do not need to know the distribution of the returns/price

A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. A free-boundary value approach is adopted and the value function is obtained via fundamental solution methods. There are many applications for the valuation of...

In this paper, we propose a novel model for pricing double barrier options, where the asset price is modeled as a threshold geometric Brownian motion time changed by an integrated activity rate process, which is driven by the convolution of a fractional kernel with the CIR process. The new model...

Bitcoin Pricing Kernels (PKs) are estimated using a novel data set from Deribit, the leading Bitcoin options exchange. The PKs, as the ratio between risk-neutral and physical density, dynamically reflect the change in investor preferences. Thus, the PKs improve the understanding of investor...

This paper discusses the generalized Black-Scholes-Merton model, where the volatility coefficient, the drift coefficient of stocks, and the interest rate are time-dependent deterministic functions. Together with it, we make the assumption that the volatility, the drift, and the interest rate...

We extend the short rate model of Turfus and Romero-Bermúdez [2021] to facilitate accurate arbitrage-free analytic pricing of SOFR, SONIA or ESTR caplets, i.e. options on backward-looking compounded rates payments, in a manner consistent with the smile and skew levels observed in the market....

Fukasawa introduced in [Fukasawa, Math Financ, 2012] two necessary conditions for no butterfly arbitrage which require that the $d_1$ and $d_2$ functions of the Black-Scholes formula have to be decreasing. In this article we characterize the set of smiles satisfying these conditions, using the...

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...

We observe that a European Call option with strike $L K$ can be seen as a Call option with strike $L-K$ on a Call option with strike $K$. Under no arbitrage assumptions, this yields immediately that the prices of the two contracts are the same, in full generality. We study in detail the...

Determining optimal exercise boundaries has been central to pricing American options. Ingersoll (1998) offers an alternative to approximating option prices using simple barrier derivatives. Using pricing formulas for multi-step barrier options with a rebate, we generalize it to value American...