Journal Article10.1111/J.1540-6261.1985.TB02383.X
Option Pricing and Replication with Transactions Costs
TL;DR: In this paper, a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision was developed, which permits calculation of the transactions costs of option replication and provides bounds on option prices.
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Abstract: Transactions costs invalidate the Black-Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. Discrete revision using Black-Scholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. This paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision. The technique permits calculation of the transactions costs of option replication and provides bounds on option prices.
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Citations
Informed Trading and Option Spreads
TL;DR: In this article, the authors assess the presence and nature of strategic trading by informed investors in the options market and find that the adverse selection component of the underlying stock's spread explains a significant fraction of the option spread.
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Static Hedging of Standard Options
Peter Carr,Liuren Wu +1 more
TL;DR: In this article, the authors consider the hedging of options when the underlying asset price is exposed to the possibility of jumps of random size and derive a new, static spanning relation between a given option and a continuum of shorter-term options written on the same asset.
Stochastic Dominance Bounds on Derivative Prices in a Multiperiod Economy with Proportional Transaction Costs
TL;DR: By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds onThe reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security.
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Financial asset-pricing theory and stochastic programming models for asset/liability management: a synthesis
TL;DR: In this article, the authors present aggregation methods which can be used in combination with nancial asset-pricing models to obtain a description of the uncertainty that is arbitrage-free, consistent with observed market prices as well as concise enough for a stochastic programming model.
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On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance
TL;DR: The implicit-explicit (IMEX) two-step backward differentiation formula (BDF2) method with variable step-size, due to the nonsmoothness of the initial data, is developed for solving backward differentiation problems.
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References
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
31.9K
An introduction to probability theory and its applications - 3/E. volume 3
William Feller
- 22 Mar 2002
Abstract: The classic text for understanding complex statistical probability An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivreLaplace theorem.
21.5K
The Valuation of Uncertain Income Streams and the Pricing of Options
TL;DR: In this paper, a simple formula for the valuation of uncertain income streams consistent with rational risk averse investor behavior and equilibrium in financial markets is developed for the pricing of an option as a function of its associated stock.
1.6K