Dynamic Programming Algorithms for the Ask and Bid Prices of American Options Under Small Proportional Transaction Costs PDF Download
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Author: Tomasz Zastawniak
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
Dynamic programming algorithms are developed for computing the ask and bid prices of American contingent claims in a binary tree setting in the presence of small proportional transaction costs, extending the recursive construction of the Snell envelope. Associated with the pricing algorithms are iterative procedures for computing optimal hedging strategies for the writer as well as for the buyer of an American option. The bid and ask prices of an American option are represented in terms of the expectation of the option payoff evaluated at an optimal stopping time with respect to an optimal martingale probability measure. As a by-product a similar dynamic programming algorithm is obtained for pricing and hedging European contingent claims in the same setting.
Author: Tomasz Zastawniak
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
Dynamic programming algorithms are developed for computing the ask and bid prices of American contingent claims in a binary tree setting in the presence of small proportional transaction costs, extending the recursive construction of the Snell envelope. Associated with the pricing algorithms are iterative procedures for computing optimal hedging strategies for the writer as well as for the buyer of an American option. The bid and ask prices of an American option are represented in terms of the expectation of the option payoff evaluated at an optimal stopping time with respect to an optimal martingale probability measure. As a by-product a similar dynamic programming algorithm is obtained for pricing and hedging European contingent claims in the same setting.
Author: Tomasz Zastawniak
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
American options exercised by physical delivery of a portfolio of cash and underlying stock are considered in the binary tree model under small proportional transaction costs. Dynamic programming type recursive algorithms are developed for computing the ask and bid prices of such options, extending the Snell envelope construction. Representations of the ask and bid prices of American options with physical delivery in terms of maximax and, respectively, maximin martingale expectations of stopped option payoffs are also established in this setting.
Author: Tomasz Zastawniak
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
American options are priced and hedged in a general discrete market in the presence of arbitrary proportional transaction costs inherent in trading the underlying asset, modelled as bid-ask spreads. Pricing, hedging and optimal stopping algorithms are established for a short position (seller's position) in an American option with an arbitrary payoff settled by physical delivery. The seller's price representation as the expectation of the stopped payoff under an approximate martingale measure is also considered. The algorithms cover and extend the various special cases considered in the literature to-date. Any specific restrictions that were imposed on the form of the payoff, the magnitude of transaction costs or the discrete market model itself are relaxed. The pricing algorithm under transaction costs can be viewed as a natural generalisation of the iterative Snell envelope construction.
Author: 宋娜
Publisher:
ISBN: 9781361322062
Category :
Languages : en
Pages :
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This dissertation, "Mathematical Models and Numerical Algorithms for Option Pricing and Optimal Trading" by Na, Song, 宋娜, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis. The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem. Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It's also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively. DOI: 10.5353/th_b5066216 Subjects: Options (Finance) - Prices - Mathematical models Options (Finance) - Mathematical models
Author: Roberto Baviera
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
We provide closed formulas for European call option ask and bid prices in presence of transaction costs. Underlying prices have the same dynamics of Black-Scholes model and a bid-ask spread proportional to bid price. We suppose that a market maker has to quote a bid and ask price for an option in a perfect competition market. Under these conditions derivative prices are obtained imposing the No Almost Sure Arbitrage Principle: the market maker fixes bid (ask) price as the highest buying (lowest selling) price that can accepted by an investor who maximizes the growth rate of his portfolio.
Author: Valeriy Zakamulin
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal transaction policy of the option holder. We examine the effects on the reservation option prices and the corresponding exercise policies of varying the levels of absolute risk aversion and transaction costs.
Author: Leonid Kogan
Publisher:
ISBN:
Category :
Languages : en
Pages : 76
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Book Description
We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest. Keywords: Asset pricing, dynamic programming, simulation, American option, optimal stopping, duality.
Author: Q. Shen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 378
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Author: 葉雲軒
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
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