Utility-Based Valuation and Hedging of Basis Risk With Partial Information

Monoyios, Michael

doi:10.1080/13504861003650883

Cited by 14 publications

(11 citation statements)

References 26 publications

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“…In what follows we assume that the indifference price is a suitably smooth function of (t, s, y), so that (given Lemma 3) we may assume the primal value function is smooth enough to be a classical solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. This smoothness property is confirmed in [24].…”

Section: Optimal Hedging Of Basis Risk With Partial Informationsupporting

confidence: 66%

“…In [24] these results are used to conduct a simulation study of the effectiveness of the optimal hedge under partial information (that is, with Bayesian learning about the drift parameters of the assets), compared with the BS-style hedge and the optimal hedge without learning. The results show that optimal hedging combined with a filtering algorithm to deal with drift parameter uncertainty can indeed give improved hedging performance over methods which take S as a perfect proxy for Y , and over methods which do not incorporate learning via filtering.…”

Section: Optimal Hedging Of Basis Risk With Partial Informationmentioning

confidence: 99%

“…These are hard to estimate accurately, as shown by Rogers [31] and Monoyios [23], who showed that drift parameter mis-estimation could ruin the effectiveness of the optimal hedge. Finally, in [24,26] Monoyios developed a filtering algorithm to deal with the drift parameter uncertainty, and showed that with this added ingredient, utility-based hedging was indeed effective, even in the face of parameter uncertainty. We shall describe some of these results in this section.…”

Section: Computing the Information Driftmentioning

confidence: 99%

“…Analytic approximations for prices and hedging strategies are given. Further work on this topic can be found in Monoyios [24,26].…”

Section: Introductionmentioning

confidence: 99%

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Optimal investment and hedging under partial and inside information

Albrecher¹,

Runggaldier²,

Schachermayer³

2009

Advanced Financial Modelling

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This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time 0 of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy.

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Section: Optimal Hedging Of Basis Risk With Partial Informationsupporting

confidence: 66%

Section: Optimal Hedging Of Basis Risk With Partial Informationmentioning

confidence: 99%

Section: Computing the Information Driftmentioning

confidence: 99%

“…Analytic approximations for prices and hedging strategies are given. Further work on this topic can be found in Monoyios [24,26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal investment and hedging under partial and inside information

Albrecher¹,

Runggaldier²,

Schachermayer³

2009

Advanced Financial Modelling

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show abstract

“…Our goal is to compute the optimal strategy θ L, * achieving the supremum in (25) as well as the value function u L , for three particular cases of L, and hence three choices of filtration F L , as listed below.…”

Section: The Utility Maximisation Problemsmentioning

confidence: 99%

Optimal investment with inside information and parameter uncertainty

Danilova¹,

Monoyios²,

Ng³

2010

Math Finan Econ

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An optimal investment problem is solved for an insider who has access to noisy information related to a future stock price, but who does not know the stock price drift. The drift is filtered from a combination of price observations and the privileged information, fusing a partial information scenario with enlargement of filtration techniques. We apply a variant of the Kalman-Bucy filter to infer a signal, given a combination of an observation process and some additional information. This converts the combined partial and inside information model to a full information model, and the associated investment problem for HARA utility is explicitly solved via duality methods. We consider the cases in which the agent has information on the terminal value of the Brownian motion driving the stock, and on the terminal stock price itself. Comparisons are drawn with the classical partial information case without insider knowledge. The parameter uncertainty results in stock price inside information being more valuable than Brownian information, and perfect knowledge of the future stock price leads to infinite additional utility. This is in contrast to the conventional case in which the stock drift is assumed known, in which perfect information of any kind leads to unbounded additional utility, since stock price information is then indistinguishable from Brownian information.

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Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information

Yang

2011

Comput Econ

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This paper extends real options theory to consider the situation where the mean appreciation rate of the value of an irreversible investment project is not observable and governed by an Ornstein-Uhlenbeck process. Our main purpose is to analyze the impact of the uncertainty of the mean appreciation rate on the pricing and investment timing of the option to invest under incomplete markets with partial information. We assume that an investor aims to maximize expected discounted utility of lifetime consumption. Based on consumption utility indifference pricing method, stochastic control and filtering theory, we obtain under CARA utility the implied values and the optimal investment thresholds of the option to invest, which are determined by a semi-closed-form solution to a free-boundary partial differential equation (PDE) problem. The solution is independent of the utility time-discount rate. We provide numerical results by finite difference methods and compare the results with those under a fully observable case. Numerical calculations show that partial information leads to a significant loss of the implied value of the option to invest. This loss, called implied information value, IIV increases quickly with the uncertainty of the mean appreciation rate. A high volatility of project values might decrease the IIV, as well as the implied value of the option.

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Utility-Based Valuation and Hedging of Basis Risk With Partial Information

Cited by 14 publications

References 26 publications

Optimal investment and hedging under partial and inside information

Optimal investment and hedging under partial and inside information

Optimal investment with inside information and parameter uncertainty

Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information

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