Related papers: Option Pricing in an Investment Risk-Return Settin…
Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk,…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies…
An empirical analysis, suggested by optimal Merton dynamics, reveals some unexpected features of asset volumes. These features are connected to traders' belief and risk aversion. This paper proposes a trading strategy model in the optimal…
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…
It is well-known that using delta hedging to hedge financial options is not feasible in practice. Traders often rely on discrete-time hedging strategies based on fixed trading times or fixed trading prices (i.e., trades only occur if the…
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as…
This paper considers the optimal portfolio selection problem in a dynamic multi-period stochastic framework with regime switching. The risk preferences are of exponential (CARA) type with an absolute coefficient of risk aversion which…
I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with Student-t…
Portfolio construction is the science of balancing reward and risk; it is at the core of modern finance. In this paper, we tackle the question of optimal decision-making within a Bayesian paradigm, starting from a decision-theoretic…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…
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…
We examine the possibility of incorporating information or views of market movements during the holding period of a portfolio, in the hedging of European options with respect to the underlying. Given a fixed holding period interval, we…
We study the problem of optimal portfolio selection in an illiquid market with discrete order flow. In this market, bids and offers are not available at any time but trading occurs more frequently near a terminal horizon. The investor can…
In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics.…
We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a…
In this report we derive the strategic (deterministic) allocation to bonds and stocks resulting in the optimal mean-variance trade-off on a given investment horizon. The underlying capital market features a mean-reverting process for equity…