1,720,971 research outputs found
On the singular control of exchange rates
Full text linkFerrari G, Vargiolu T. On the singular control of exchange rates. Annals of Operations Research. 2020;292:795-832.Consider a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each direct intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current level of the exchange rate. The central bank aims at minimizing the total expected costs of interventions on the exchange market, plus a total expected running cost. We formulate this problem as an infinite time-horizon bounded-variation stochastic control problem. The exchange rate evolves as a general one-dimensional diffusion, and it is linearly controlled by two nondecreasing processes modeling the cumulative amount of foreign currency that has been purchased and sold by the central bank. We provide a complete solution to this problem by finding the explicit expression of the value function and a complete characterization of the optimal control. At each instant of time, the optimally controlled exchange rate is kept within a band whose size is endogenously determined as part of the solution to the problem. We also study the expected exit time from the band, and the sensitivity of the width of the band with respect to the model's parameters in the case when the exchange rate evolves (in absence of any intervention) as an Ornstein-Uhlenbeck process, and the marginal proportional costs of controls are constant. The techniques employed in the paper are those of the theory of singular stochastic control and of one-dimensional diffusions
Price dynamics in the European Union Emissions Trading System and evaluation of its ability to boost emission-related investment decisions
Full text linkThe price of permits in the European Union Emissions Trading System (EU ETS) has historically been highly sensitive and prone to jumps. We consider different stochastic processes to model the price of permits, and show that the Variance Gamma (VG) model provides the best fit for the price distribution, among a selection of infinite activity processes. Using this result as a starting point, we assess the effects of the EU ETS in delivering low-carbon investments at the firm level, by modeling a price taker electricity producer subject to the EU ETS jurisdiction. We compute, via Least Squares Monte Carlo, the value of the real option the greenhouse gas emitter has, consisting in the opportunity to switch from its current high-carbon technology to a cleaner one. We use a VG specification for carbon prices, and a mean-reverting (Brennan–Schwartz) process for the price of fuel. Moreover, we further analyze the investment decision problem, in case of a CO2 price stabilization mechanism in th..
Un approccio Bayesiano alla gestione del rischio in un modello binomiale.
No full textIn questo lavoro si considera, per un modello a tempo discreto, il problema di minimizzazione dello scoperto medio di portafoglio qualora un agente finanziario, accettando qualche rischio, scelga di investire un capitale iniziale inferiore a quello di copertura. Si analizza la duplice situazione in cui la legge che governa la dinamica del titolo rischioso sottostante e' completamente oppure parzialmente nota. In quest'ultimo caso, si adotta l'appoccio adattativo bayesiano descritto in [25]. Nel caso particolare di un modello binomiale, seguendo [24] si derivano formule esplicite sia per lo scoperto ottimale di portafoglio sia per la corrispondente strategia ottimale. Le soluzioni trovate risultano essere una intuitiva estensione di quelle per il classico modello di Cox-Ross-Rubinstein. Vengono poi presentate ulteriori direzioni di ricerca
Optimal installation of solar panels with price impact: A solvable singular stochastic control problem
Full text linkWe consider a price-maker company which generates electricity and sells it in the spot market. The company can increase its level of installed power by irreversible installations of solar panels. The electricity price evolves as an Ornstein Uhlenbeck process, whose drift is negatively impacted by the current level of the company s installed power. The company aims at maximizing the total expected profits from selling electricity in the market, net of the total expected proportional costs of installation. This problem is modeled as a two-dimensional degenerate singular stochastic control problem. We find that the optimal installation strategy is triggered by a curve which separates the waiting region, where it is not optimal to install additional panels, and the installation region, where it is. Such a curve is the unique strictly increasing solution of a first-order ordinary differential equation. Finally, we show numerically the dependence of the optimal installation strategy on the model s parameters
A Bayesian adaptive control approach to risk management in a binomial model
No full textWe consider the problem of shortfall risk minimization when there is uncertainty about the exact stochastic dynamics of the underlying. Starting from the general discrete time model and the approach described in Runggaldier and Zaccaria (1999), we derive explicit analytic solutions for the particular case of a binomial model when there is uncertainty about the probability of an "up-movement". The solution turns out to be a rather intuitive extension of that for the classical Cox-Ross-Rubinstein model
Optimal installation of renewable electricity sources: the case of Italy
Full text linkStarting from the model in Koch-Vargiolu (2019), we test the real impact of
current renewable installed power in the electricity price in Italy, and assess
how much the renewable installation strategy which was put in place in Italy
deviated from the optimal one obtained from the model in the period 2012--2018.
To do so, we consider the Ornstein-Uhlenbeck (O-U) process, including an
exogenous increasing process influencing the mean reverting term, which is
interpreted as the current renewable installed power. Using real data of
electricity price, photovoltaic and wind energy production from the six main
Italian price zones, we estimate the parameters of the model and obtain
quantitative results, such as the production of photovoltaic energy impacts the
North zone, while wind is significant for Sardinia and the Central North zone
does not present electricity price impact. Then we implement the solution of
the singular optimal control problem of installing renewable power production
devices, in order to maximize the profit of selling the produced energy in the
market net of installation costs. We extend the results of \cite{KV} to the
case when no impact on power price is presented, and to the case when
players can produce electricity by installing renewable power plants. We are
thus able to describe the optimal strategy and compare it with the real
installation strategy that was put in place in Italy
Robustness for path-dependent volatility models
No full textIn this paper, we consider a generalisation of the Hobson-Rogers model proposed by Foschi and Pascucci (Decis Eocon Finance 31(1):1-20, 2008) for financial markets where the evolution of the prices of the assets depends not only on the current value but also on past values. Using differentiability of stochastic processes with respect to the initial condition, we analyse the robustness of such a model with respect to the so-called offset function, which generally depends on the entire past of the risky asset and is thus not fully observable. In doing this, we extend previous results of Blaka Hallulli and Vargiolu (2007) to contingent claims, which are globally Lipschitz with respect to the price of the underlying asset, and we improve the dependence of the necessary observation window on the maturity of the contingent claim, which now becomes of linear type, while in Blaka Hallulli and Vargiolu (2007), it was quadratic. Finally, in this framework, we give a characterisation of the stationarity assumption used in Blaka Hallulli and Vargiolu (2007), and prove that this model is stationary if and only if it is reduced to the original Hobson-Rogers model. We conclude by calibrating the model to the prices of two indexes using two different volatility shapes. © 2012 Springer-Verlag
Robustness of shortfall risk minimising strategies in the binomial model
No full textIn this paper we study the dependence on the loss function of the strategy which minimises the expected shortfall risk when dealing with a financial contingent claim in the particular situation of a binomial model. After having characterised the optimal strategies in the particular cases when the loss function is concave, linear or strictly convex, we analyse how optimal strategies change when we approximate a loss function with a sequence of suitable loss functions
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