Related papers: A New Approach to Model Free Option Pricing
We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the…
We show how inter-asset dependence information derived from market prices of options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the traded option, we either extract correlation…
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…
We propose an innovative data-driven option pricing methodology that relies exclusively on the dataset of historical underlying asset prices. While the dataset is rooted in the objective world, option prices are commonly expressed as…
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…
We propose three different data-driven approaches for pricing European-style call options using supervised machine-learning algorithms. These approaches yield models that give a range of fair prices instead of a single price point. The…
We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the…
In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
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…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
We consider the superhedging price of an exotic option under nondominated model uncertainty in discrete time in which the option buyer chooses some action from an (uncountable) action space at each time step. By introducing an enlarged…
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
We present a high-level framework that explains why, in practice, different pricing models calibrated to the same vanilla surface tend to produce similar valuations for exotic derivatives. Our approach acts as an overlay on the Monte Carlo…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
We develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem: asymmetric options' distributions, high dimensionality and dependence structure. To do so, we propose a new…
In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via…