Study Of Randomized American Option Pricing Based On Martingale Analysis

The problem of American option pricing is one of the important researchtopics in recent financial statistics. Due to American option can be executedbefore the maturity date, so its pricing is much more difficult than the European’s.By deep study of the characteristics of American options and their pricesformation mechanism, the text focus on the description of how to apply themartingale analysis to come to the American option price formula, and randomlyunder executing the price of options, the optimal underlying asset pricingformula is determined. With greater practicality than the fixed exercise price, it isthe modelsimportant of option pricing to promote.Departuring from the theoretical and practical significance of the optionpricing background and to study the subject, this text studies the methods of thegeneral pricing options on the basis of the research situation and researchmethods, and explores and comes to the general advantages of the interest ratesand stocks to follow the generalized O-U process model comparing to followingthe Brown motion model and the B-S pricing model. Following the O-U processmodel, the study analyzes the relationship between future stock price, and makefull use of the equivalent martingale measure transform, in the condition o foptions expected rate of return and stock price volatility when in doubt, obtains astochastic exercise price of American call and put option pricing formula. Alsounder the situation of the option exercises price randomly, according to therelevant theory of martingale analysis to determined the formula of call and putoption with default risk, to study the option pricing problem this paper presents aresearch method.Using martingale analysis in the random case of the American optionexercise price, the option pricing formula derived from a more general, at last inthe random case of the American option exercise price, it obtains the most the priority of the underlying asset pricing formula. Conclusion is not only theapplication of the martingale, but also of great significance in financial statistics.