Options & Derivatives Pricing

The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of the multivariate process of constituents with a copula model

The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a rigorous analysis of hedge errors within the Black-Scholes fram

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only on the inputs and labels but also the differentials of the c

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 stochastic Taylor expansion around a log-normal proxy model and a

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for different behaviours across various times or regimes. To establ

We propose a numerical procedure for computing the prices of European options, in which the underlying asset price is a Markovian strict local martingale. If the underlying process is a strict local martingale and the payoff is of linear growth, multiple solutions exist for the corresponding Black-S

This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely concerned in the option market. Departing from conventional proce

This study enhances option pricing by presenting unique pricing model fractional order Black-Scholes-Merton (FOBSM) which is based on the Black-Scholes-Merton (BSM) model. The main goal is to improve the precision and authenticity of option pricing, matching them more closely with the financial land

For vanilla derivatives that constitute the bulk of investment banks’ hedging portfolios, central clearing through central counterparties (CCPs) has become hegemonic. A key mandate of a CCP is to provide an efficient and proper clearing member default resolution procedure. When a clearing member def

In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton–Jacobi–Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic control may be undesirable for various business reasons. In this

In this paper similar to [“P. Carr, A. Itkin, 2019”] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both risk-neutral and real measures which is an unsteady three-dimensiona

We discover several surprising relationships between large classes of seemingly unrelated foundational problems of financial engineering and fundamental problems of hydrodynamics and molecular physics. Solutions in all these domains can be reduced to solving affine differential equations commonly us

This paper introduces the concept of a global financial market for environmental indices, addressing sustainability concerns and aiming to attract institutional investors. Risk mitigation measures are implemented to manage inherent risks associated with investments in this new financial market. We m

We study the problem of valuing and hedging a vulnerable derivative claim with bilateral cash flows between two counterparties in the presence of asymmetric funding costs, defaults and wrong way risk (WWR). We characterize the pre-default claim value as the solution to a non-linear Cauchy problem. W

Crowding is widely regarded as one of the most important risk factors in designing portfolio strategies. In this paper, we analyze stock crowding using network analysis of fund holdings, which is used to compute crowding scores for stocks. These scores are used to construct costless long-short portf

In this paper, we provide an overview of the recent work in the quantum finance realm from various perspectives. The applications in consideration are Portfolio Optimization, Fraud Detection, and Monte Carlo methods for derivative pricing and risk calculation. Furthermore, we give a comprehensive ov

Investors always want to know about the profit and the risk that they will be get before buying some assets. Our main focus is getting the profit and the probability of getting that profit using the differential evolution algorithm for vanilla option pricing on data before and during COVID-19 pandem

We derive the explicit price of the perpetual American put option cancelled at the last passage time of the underlying above some fixed level. We assume the asset process is governed by a geometric spectrally negative Lévy process. We show that the optimal exercise time is the first epoch when asset

We apply rough-path theory to study the discrete-time gamma-hedging strategy. We show that if a trader knows that the market price of a set of European options will be given by a diffusive pricing model, then the discrete-time gamma-hedging strategy will enable them to replicate other European optio

We consider the multiple quantile hedging problem, which is a class of partial hedging problems containing as special examples the quantile hedging problem (F{“ö”}llmer & Leukert 1999) and the PnL matching problem (introduced in Bouchard & Vu 2012). In complete non-linear markets, we show that the p