Related papers: Pricing and hedging American-style options with de…
A number of Bermudan option pricing methods that are applicable to options on multiple assets are studied in this thesis, one of the dominating questions being the natural scaling needed to extrapolate from Bermudan to American (both…
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…
We propose a reinforcement learning (RL) approach to model optimal exercise strategies for option-type products. We pursue the RL avenue in order to learn the optimal action-value function of the underlying stopping problem. In addition to…
The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives…
In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…
We present a semi-static hedging algorithm for callable interest rate derivatives under an affine, multi-factor term-structure model. With a traditional dynamic hedge, the replication portfolio needs to be updated continuously through time…
There exist several methods how more general options can be priced with call prices. In this article, we extend these results to cover a wider class of options and market models. In particular, we introduce a new pricing formula which can…
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $\pi$ is given…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
This paper explores the application of deep Q-learning to hedging at-the-money options on the S\&P~500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
The Heston stochastic volatility model is a widely used tool in financial mathematics for pricing European options. However, its calibration remains computationally intensive and sensitive to local minima due to the model's nonlinear…
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed…
This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual…
We give an analytical characterization of the price function of an American option in Heston-type models. Our approach is based on variational inequalities and extends recent results of Daskalopoulos and Feehan (2011). We study the…
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…
We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility…
We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity,…