The American Put Option Valued Analytically

Geske, Robert; Johnson, H. E.

doi:10.2307/2327741

Cited by 206 publications

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“…We assume that 2 Geske and Johnson (1984) have provided the pricing formula for the American put option with a finite maturity. Moreover, our model assumes that the value of the post-development option is conditional on the pre-moratorium option not being exercised.…”

Section: Basic Assumptionsmentioning

confidence: 99%

How Does a Development Moratorium Affect Development Timing Choices and Land Values?

Jou

Lee

2009

J Real Estate Finan Econ

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Section: Basic Assumptionsmentioning

confidence: 99%

How Does a Development Moratorium Affect Development Timing Choices and Land Values?

Jou

Lee

2009

J Real Estate Finan Econ

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“…An American call is therefore equivalent to a European call and can be priced in O(n) time. Thus much research has focused on devising fast pricing methods for American puts [20], [13], [6]. It is known [10] that the value of an American perpetual put (APP) can be computed in O(1) time.…”

Section: Approximating An N-period American Put With a Perpetual Putmentioning

confidence: 99%

Approximate Option Pricing

Chalasani¹,

Jha²,

Saias³

1999

Algorithmica

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As increasingly large volumes of sophisticated options are traded in world financial markets, determining a "fair" price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte Carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs.In this article we show that pricing an arbitrary path-dependent option is #-P hard. We show that certain types of path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these we design deterministic polynomial-time approximate algorithms. We show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation of the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, our algorithms have guaranteed error bounds that are polynomially small (and in some cases exponentially small) in the maturity n. For the error analysis we derive large-deviation results for random walks that may be of independent interest.

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“…McDonald and Siegel's (1985) model values an European exchange option considering that the assets distribute dividends. Carr (1988) develops a model to value an American exchange option using the Geske and Johnson (1984) approximation for valuing American puts, and he presents also a model to value an European compound exchange option. Finally, Armada et al (2007) correct the Carr's extrapolation formula to value an American exchange option.…”

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confidence: 99%

An R&D Investment Game under Uncertainty in Real Option Analysis

Villani

2008

Comput Econ

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One of the problems of using the financial options methodology to analyse investment decisions is that strategic considerations become extremely important. So, the theory of real option games combines two successful theories, namely real options and game theory. The investment opportunity and the value of flexibility can be valued as a real option while the competition can be analyzed with game theory. In our model we develop an interaction between two firms that invest in R&D. The firm that invests first, defined as the Leader, acquires a first mover advantage that we assume as a higher share of market. But, several R&D investments present positive externalities and so, the option exercise by the Leader generates an “Information Revelation”, that benefits the Follower

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The American Put Option Valued Analytically

Cited by 206 publications

References 0 publications

How Does a Development Moratorium Affect Development Timing Choices and Land Values?

How Does a Development Moratorium Affect Development Timing Choices and Land Values?

Approximate Option Pricing

An R&D Investment Game under Uncertainty in Real Option Analysis

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