Approximating the Optimal Exercise Boundary for American Options via Least-Squares Monte Carlo PDF Download
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Author: Qiang Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
The least-squares Monte Carlo method of Longstaff-Schwartz is utilized to construct the optimal exercise boundary (OXB) of an American put option when the underlying follows a geometric Brownian motion (GBM). The optimal exercise price at each time step is obtained by solving numerically the equation of the exercising boundary condition. The set of such exercise prices, along with their ldquo;standard deviations,rdquo; is then fitted to a smooth, monotonic model of a sum of three exponential functions to approximate the OXB, which turns out to be very close to the exact solution of the boundary. The approach can be efficiently implemented and readily computed in practice, and should be applicable to cases when the underlying price process is not GBM.
Author: Qiang Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
The least-squares Monte Carlo method of Longstaff-Schwartz is utilized to construct the optimal exercise boundary (OXB) of an American put option when the underlying follows a geometric Brownian motion (GBM). The optimal exercise price at each time step is obtained by solving numerically the equation of the exercising boundary condition. The set of such exercise prices, along with their ldquo;standard deviations,rdquo; is then fitted to a smooth, monotonic model of a sum of three exponential functions to approximate the OXB, which turns out to be very close to the exact solution of the boundary. The approach can be efficiently implemented and readily computed in practice, and should be applicable to cases when the underlying price process is not GBM.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The fast advancement in computer technologies in the recent years has made the use of simulation to estimate stock/equity performances and pricing possible; however, determining the optimal exercise time and prices of American options using Monte-Carlo simulation is still a computationally challenging task due to the involved computer memory and computational complexity requirements. At each time step, the investor must decide whether to exercise the option to get the immediate payoff, or hold on to the option until a later time. Traditionally, the stock options are simulated using Monte-Carlo methods and all stock prices along the path are stored, and then the optimal exercise time is determined starting at the final time period and continuing backward in time. Also, as the number of paths simulated increases, the number of simultaneous equations that need to be solved at each time step grow proportionally. Currently, two theoretical methods have emerged in determining the optimal exercise problem. The first method uses the concept of least-squares approach in linear regression to estimate the value of continuing to hold on to the option via a set of randomly generated future stock prices. Then, the value of continuing can be compared to the payoff at current time from exercising the option and a decision can be reached, which gives the investor a higher value. The second method uses the finite difference approach to establish an exercise boundary for the American option via an artificially generated mesh on both possible stock prices and decision times. Then, the stock price is simulated and the method checks to see if it is inside the exercise boundary. In this research, these two solution approaches are evaluated and compared using discrete event simulation. This allows complex methods to be simulated with minimal coding efforts. Finally, the results from each method are compared. Although a more conservative method cannot be determined, the least-squares method is faster, more concise, easier to implement, and requires less memory than the mesh method. The motivation for this research stems from interest in simulating and evaluating complicated solution methods to the optimal exercise problem, yet requiring little programming effort to produce accurate and efficient estimation results.
Author: Song-Ping Zhu
Publisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 9
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Book Description
Author: Victoria Zhanna Averbukh
Publisher:
ISBN:
Category : Finansielle instrumenter
Languages : en
Pages : 138
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
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Book Description
Author: Yue-Kuen Kwok
Publisher: Springer Science & Business Media
ISBN: 3540686886
Category : Mathematics
Languages : en
Pages : 541
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Book Description
This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.
Author: Andreas Andrikopoulos
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The valuation of put options with early-exercise opportunities constitutes a major challenge of asset pricing. The option-theoretic response to this challenge relies on the estimation of the optimal exercise boundary. This paper introduces a novel quadratic approximation for the valuation of American options on common stock. The paper's contribution lies in the tradition of semi-analytical approximation of American put options, which was put forward in Barone-Adesi and Whaley (1987). Assuming that the interest rate and the volatility are constant, the early-exercise premium is modeled as a product of two functions, one being a function of time and the other being a function of the stock price. The numerical results demonstrate the accuracy of the method, over competing alternatives such as the Barone-Adesi and Whaley (1987) algorithm.
Author: David Animante
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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Book Description
The use of American style equity options as hedging instrument has gained currency in recent times. This phenomenon devolves from the ever-expanding need by individuals, corporations and governments to hedge away their financial risks and the clarion call for derivative securities that give the holder increased flexibility in exercise. Nevertheless, pricing American options is complex and there exists no analytic solution to the problem except a profusion of approximation and finite difference techniques. Indeed, many researchers have shown that these methods cannot handle multifactor situations where the underlying asset follows a jump-diffusion process and where the derivative security depends on multiple sources of uncertainty such as stochastic volatility, stochastic interest rate among others. Monte-Carlo simulation techniques therefore developed out of the search for a pricing formula that has the capacity to accommodate all forms of uncertainty and at the same time able to produce speedy and accurate results. Some scholars at first rejected these techniques as yielding inaccurate results but in recent times, many researchers have demonstrated the efficacy of Monte-Carlo simulation in option pricing. The aim of this study is to assess the effectiveness of Monte-Carlo simulation methods in comparison with other option pricing techniques. To achieve this objective, the research builds an algorithm to compute Call and Put prices based on a wide range of input parameters. It also develops a model where volatility or interest rate is stochastic and a deterministic function of time. The results indicate that Monte-Carlo simulation techniques produce option values and exercise boundaries that are very similar to the Binomial, Barone-Adesi and Whaley as well as the Explicit Finite Difference methods. The results also show that the stochastic volatility and stochastic interest rate models yield slightly different but more accurate results. Consequently, the study recommends simulation techniques that incorporate multiple sources of uncertainty simultaneously for fast, efficient and more accurate option pricing.
Author: 黃惠君
Publisher:
ISBN:
Category :
Languages : zh-CN
Pages : 102
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Book Description
Author: Lei Zhang
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 284
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Book Description
