Related papers: Hedging Swing contract on gas markets
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
Electricity market mechanisms designed to steer sustainable generation of electricity play an important role for the energy transition intended to mitigate climate change. One of the major problems is to complement volatile renewable energy…
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices…
In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial,…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
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…
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in…
We propose two parametric approaches to evaluate swing contracts with firm constraints. Our objective is to define approximations for the optimal control, which represents the amounts of energy purchased throughout the contract. The first…
In this short note, we will show how to optimize the portfolio of a large trader whose hedging strategy affects the price of his assets.
This work addresses the problem of optimal pricing and hedging of a European option on an illiquid asset Z using two proxies: a liquid asset S and a liquid European option on another liquid asset Y. We assume that the S-hedge is dynamic…
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…
A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so,…
The wide adoption of gas fired units and power-to-gas technology brings remarkable interdependency between natural gas and electricity infrastructures. This paper studies the equilibria of coupled gas and electricity energy markets driven…
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward…
Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the…
This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…
We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on…
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable.…
In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A…
We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the…