Related papers: Model-Free Discretisation-Invariant Swap Contracts
We derive a general multivariate theory for realised characteristics of `model-free discretisation-invariant swaps', so-called because the standard no-arbitrage assumption of martingale forward prices is sufficient to derive fair-value swap…
A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In…
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically…
We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull-White and Schobel-Zhu stochastic volatility models we give simple explicit expressions…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.…
Discretely sampled variance and volatility swaps trade actively in OTC markets. To price these swaps, the continuously sampled approximation is often used to simplify the computations. The purpose of this paper is to study the conditions…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally…
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…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…