相关论文: Computation of second order price sensitivities in…

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…

We deal with the calculation of price sensitivities for stochastic volatility models. General forms for the dynamics of the underlying asset price and its volatility are considered. We make use of the chaotic (or Malliavin) calculus to…

In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…

Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…

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…

Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…

Differential sensitivity measures provide valuable tools for interpreting complex computational models used in applications ranging from simulation to algorithmic prediction. Taking the derivative of the model output in direction of a 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…

Markov decision models (MDM) used in practical applications are most often less complex than the underlying `true' MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what…

Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…

In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus which is an…

This paper deals with the computation of second or higher order greeks of financial securities. It combines two methods, Vibrato and automatic differentiation and compares with other methods. We show that this combined technique is faster…

We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…

A general market model with memory is considered in terms of stochastic functional differential equations. We aim at representation formulae for the sensitivity analysis of the dependence of option prices on the memory. This implies a…

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar…

For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…

Financial contagion has been widely recognized as a fundamental risk to the financial system. Particularly potent is price-mediated contagion, wherein forced liquidations by firms depress asset prices and propagate financial stress,…

In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to…

Sensitivity analysis plays an important role in the understanding of complex models. It helps to identify influence of input parameters in relation to the outputs. It can be also a tool to understand the behavior of the model and then can…

Differential ML (Huge and Savine 2020) is a technique for training neural networks to provide fast approximations to complex simulation-based models for derivatives pricing and risk management. It uses price sensitivities calculated through…