OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS IN LÉVY MODELS

In this paper, we extend the results of Carmona and Touzi [6] for an optimal multiple stopping problem to a market where the price process is allowed to jump. We also generalize the problem of valuation swing options to the context of a Lévy market. We prove the existence of multiple exercise policies under an additional condition on Snell envelops. This condition emerges naturally in the case of Lévy processes. Then, we give a constructive solution for perpetual put swing options when the price process has no negative jumps. We use the Monte Carlo approximation method based on Malliavin calculus in order to solve the finite horizon case. Numerical results are given in the last two sections. We illustrate the theoretical results of the perpetual case and give the numerical solution for the finite horizon case.

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MONTE CARLO DERIVATIVE PRICING WITH PARTIAL INFORMATION IN A CLASS OF DOUBLY STOCHASTIC POISSON PROCESSES WITH MARKS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024912500185 ◽

2012 ◽

Vol 15 (03) ◽

pp. 1250018

Author(s):

SILVIA CENTANNI ◽

MARCO MINOZZO

Keyword(s):

Monte Carlo ◽

Stock Price ◽

Partial Information ◽

Poisson Processes ◽

Martingale Measure ◽

Contingent Claim ◽

Filtering Algorithm ◽

Doubly Stochastic ◽

Price Process ◽

Monte Carlo Approximation

To model intraday stock price movements we propose a class of marked doubly stochastic Poisson processes, whose intensity process can be interpreted in terms of the effect of information release on market activity. Assuming a partial information setting in which market agents are restricted to observe only the price process, a filtering algorithm is applied to compute, by Monte Carlo approximation, contingent claim prices, when the dynamics of the price process is given under a martingale measure. In particular, conditions for the existence of the minimal martingale measure Q are derived, and properties of the model under Q are studied.

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A Study on Optimal Multiple Stopping and Swing Options Pricing

GANIT Journal of Bangladesh Mathematical Society ◽

10.3329/ganit.v40i2.51317 ◽

2021 ◽

Vol 40 (2) ◽

pp. 145-155

Author(s):

Atoshi Das ◽

ABM Shahadat Hossain

Keyword(s):

Monte Carlo ◽

Numerical Methods ◽

Finite Difference ◽

Random Process ◽

Optimal Stopping ◽

Electricity Market ◽

Options Pricing ◽

Swing Options ◽

Multiple Stopping ◽

American Style

In this paper, we have studied the optimal stopping of random process as well as the costing of Swing options, specially the valuation of electricity market which is considered to an American style option having multiple practicing rights. Since this type of options are widely used in investing, so it requires some methods for valuation and that should be as precise as possible. So, we discuss two numerical methods for getting swing options prices in the field of electricity market, namely Monte Carlo and Finite difference. Finally, we compare our obtained results numerically and graphically with the help of MATLAB. GANIT J. Bangladesh Math. Soc. 40.2 (2020) 145-155

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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