The Optimal Stopping Problem for a General American Put-Option

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

Advances in Data Science and Adaptive Analysis ◽

10.1142/s2424922x20500102 ◽

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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On the Continuous and Smooth Fit Principle for Optimal Stopping Problems in Spectrally Negative Lévy Models

Advances in Applied Probability ◽

10.1239/aap/1396360107 ◽

2014 ◽

Vol 46 (1) ◽

pp. 139-167 ◽

Cited By ~ 3

Author(s):

Masahiko Egami ◽

Kazutoshi Yamazaki

Keyword(s):

Optimal Stopping ◽

Optimal Stopping Problem ◽

Infinite Time ◽

Expected Payoff ◽

Threshold Levels ◽

Put Option ◽

Optimal Stopping Problems ◽

American Put ◽

Spectrally Negative Lévy Processes ◽

Optimal Candidate

We consider a class of infinite time horizon optimal stopping problems for spectrally negative Lévy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale function, and further pursue optimal candidate threshold levels. We obtain and show the equivalence of the continuous/smooth fit condition and the first-order condition for maximization over threshold levels. As examples of its applications, we give a short proof of the McKean optimal stopping problem (perpetual American put option) and solve an extension to Egami and Yamazaki (2013).

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On the Continuous and Smooth Fit Principle for Optimal Stopping Problems in Spectrally Negative Lévy Models

Advances in Applied Probability ◽

10.1017/s0001867800006972 ◽

2014 ◽

Vol 46 (01) ◽

pp. 139-167 ◽

Cited By ~ 5

Author(s):

Masahiko Egami ◽

Kazutoshi Yamazaki

Keyword(s):

Optimal Stopping ◽

Optimal Stopping Problem ◽

Infinite Time ◽

Expected Payoff ◽

Threshold Levels ◽

Put Option ◽

Optimal Stopping Problems ◽

American Put ◽

Spectrally Negative Lévy Processes ◽

Optimal Candidate

We consider a class of infinite time horizon optimal stopping problems for spectrally negative Lévy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale function, and further pursue optimal candidate threshold levels. We obtain and show the equivalence of the continuous/smooth fit condition and the first-order condition for maximization over threshold levels. As examples of its applications, we give a short proof of the McKean optimal stopping problem (perpetual American put option) and solve an extension to Egami and Yamazaki (2013).

Download Full-text