scholarly journals Optimal hitting time and perpetual option in a non-Lévy model: application to real options

2007 ◽  
Vol 39 (02) ◽  
pp. 510-530 ◽  
Author(s):  
P. Barrieu ◽  
N. Bellamy
Keyword(s):  
Optimal Stopping ◽  
Real Option ◽  
Investment Decision ◽  
Stopping Time ◽  
Investment Project ◽  
Cash Flows ◽  
Hitting Time ◽  
Optimal Stopping Time ◽  
Jump Size ◽  
The Impact

We study the perpetual American option characteristics in the case where the underlying dynamics involve a Brownian motion and a point process with a stochastic intensity. No assumption on the distribution of the jump size is made and we work with an arbitrary positive or negative jump. After proving the existence of an optimal stopping time for the problem and characterizing it as the hitting time of an optimal boundary, we provide closed-form formulae for the option value, as well as for the Laplace transform of the optimal stopping time. These results are then applied to the analysis of a real option problem when considering the impact of a fundamental and brutal change in the investment project environment. The consequences of this impact, that can seriously modify, positively or negatively, the project's future cash flows and therefore the investment decision, are illustrated by numerical examples.

scholarly journals Optimal hitting time and perpetual option in a non-Lévy model: application to real options

2007 ◽  
Vol 39 (2) ◽  
pp. 510-530 ◽  
Author(s):  
P. Barrieu ◽  
N. Bellamy
Keyword(s):  
Optimal Stopping ◽  
Real Option ◽  
Investment Decision ◽  
Stopping Time ◽  
Investment Project ◽  
Cash Flows ◽  
Hitting Time ◽  
Optimal Stopping Time ◽  
Jump Size ◽  
The Impact

We study the perpetual American option characteristics in the case where the underlying dynamics involve a Brownian motion and a point process with a stochastic intensity. No assumption on the distribution of the jump size is made and we work with an arbitrary positive or negative jump. After proving the existence of an optimal stopping time for the problem and characterizing it as the hitting time of an optimal boundary, we provide closed-form formulae for the option value, as well as for the Laplace transform of the optimal stopping time. These results are then applied to the analysis of a real option problem when considering the impact of a fundamental and brutal change in the investment project environment. The consequences of this impact, that can seriously modify, positively or negatively, the project's future cash flows and therefore the investment decision, are illustrated by numerical examples.

scholarly journals Real Option Analysis versus DCF Valuation - An Application to a Tunisian Oilfield

2019 ◽  
Vol 12 (3) ◽  
pp. 17
Author(s):  
Lotfi TALEB
Keyword(s):  
Real Option ◽  
Investment Decision ◽  
Investment Project ◽  
Cash Flows ◽  
Oil Field ◽  
Continuous Time Model ◽  
Time Model ◽  
Real Option Analysis ◽  
Real Options Approach ◽  
Proposed Model

The most widely used methods of choosing investments are undoubtedly the NPV. This method is often criticized because it does not allow to take into account certain main characteristics of the investment decision, notably the irreversibility, the uncertainty and the possibility of delaying the investment. On the other hand, the real options approach (ROA) is proposed to capture the flexibility associated with an investment project. This article examines whether the value of an undeveloped oil field varies according to whether the ROA or NPV assessment is used. In addition, to value the option to defer, we developed a continuous time model derived from previous work by Brenan and Schwartz (1985), McDonald and Siegel (1986) and Paddock, Siegel, and Smith (1988). The originality of the proposed model gives rise to a simple and uncomplicated method for determining the value of the option. Findings indicate that the two evaluation methods lead to the same decision, the project is economically profitable. In this oil investment project studied, despite the positive value of the option, the importance of projected cash-flows and optimistic forecasts of the price of oil, led us not to exercise the option and to undertake the project immediately.

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time

scholarly journals A Forward Algorithm for Solving Optimal Stopping Problems

2006 ◽  
Vol 43 (01) ◽  
pp. 102-113
Author(s):  
Albrecht Irle
Keyword(s):  
State Space ◽  
Optimal Stopping ◽  
Stopping Time ◽  
The State ◽  
Optimal Stopping Problem ◽  
Forward Algorithm ◽  
Optimal Stopping Time ◽  
Entrance Time ◽  
Markov Sequence ◽  
Optimal Stopping Problems

We consider the optimal stopping problem for g(Z n ), where Z n , n = 1, 2, …, is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B 0 ⊇ B 1 ⊇ B 2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection F of these sets is an optimal stopping time. Various applications are given.

ε - Optimal Stopping Time for Genetic Algorithms

1998 ◽  
Vol 35 (1-4) ◽  
pp. 91-111 ◽  
Author(s):  
C.A. Murthy ◽  
Dinabandhu Bhandari ◽  
Sankar K. Pal
Keyword(s):  
Genetic Algorithms ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Optimal Stopping Time

On Pricing American Put Option on a Fixed Term: A Monte Carlo Approach

2021 ◽  
pp. 2050010
Author(s):  
Perpetual Andam Boiquaye
Keyword(s):  
Monte Carlo ◽  
Optimal Stopping ◽  
Geometric Mean ◽  
Option Price ◽  
Stopping Time ◽  
Optimal Stopping Time ◽  
American Put Option ◽  
Put Option ◽  
One Year ◽  
American Put

This paper focuses primarily on pricing an American put option with a fixed term where the price process is geometric mean-reverting. The change of measure is assumed to be incorporated. Monte Carlo simulation was used to calculate the price of the option and the results obtained were analyzed. The option price was found to be $94.42 and the optimal stopping time was approximately one year after the option was sold which means that exercising early is the best for an American put option on a fixed term. Also, the seller of the put option should have sold $0.01 assets and bought $ 95.51 bonds to get the same payoff as the buyer at the end of one year for it to be a zero-sum game. In the simulation study, the parameters were varied to see the influence it had on the option price and the stopping time and it showed that it either increases or decreases the value of the option price and the optimal stopping time or it remained unchanged.

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