Related papers: Algorithmic market making for options
We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and…
This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the…
In this work we study a finite horizon optimal liquidation problem with multiplicative price impact in algorithmic trading, using market orders. We analyze the case when an agent is trading on a market with two financial assets, whose…
We present a simple order book mechanism that regulates an artificial financial market with self-organized criticality dynamics and fat tails of returns distribution. The model shows the role played by individual imitation in determining…
Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset,…
The Heston stochastic volatility model is arguably, the most popular stochastic volatility model used to price and risk manage exotic derivatives. In spite of this, it is not necessarily easy to calibrate to the market and obtain stable…
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
The paper introduces a limit version of multiple stopping options such that the holder selects dynamically a weight function that control the distribution of the payments (benefits) over time. In applications for commodities and energy…
In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a…
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 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 consider a class of optimal portfolio choice problems in continuous time where the agent's transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate…
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
In this paper, we consider the problem of optimization of a portfolio consisting of securities. An investor with an initial capital, is interested in constructing a portfolio of securities. If the prices of securities change, the investor…
We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…