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
Penalty and penalty-like methods for nonlinear HJB PDEs
TL;DR: In this paper , the authors reformulate the Hamilton-Jacobi-Bellman problem as a nonlinear PDE, involving max and min terms of the unknown function, and/or its first and second spatial derivatives, and suggest efficient numerical methods for handling the nonlinearity in the PDE through an adaptation of the discrete penalty method.
A space-time fractional derivative model for European option pricing with transaction costs in fractal market ☆
TL;DR: In this article, a modified Riemman-Liouville fractional derivative model was proposed to handle European option pricing problems with transaction costs in fractal market, and the pricing model based on a space-time fractional patrial differential equation was presented by the replicating portfolio, containing the Hurst exponent.
Option replication with transaction costs: general diffusion limits
TL;DR: In this article, the authors provide a unified methodology for calculating hedging strategies and replication errors in the small transaction cost limit, which is an essential component of optimization methods, when, for example, one is trying to minimize replication error for a given initial portfolio value.
Optimization problems in the theory of continuous trading
TL;DR: In this article, a unified approach based on stochastic analysis to the problems of option pricing, consumption/investment, and equilibrium in a financial market with asset prices modelled by continuous semi-martingales is presented.
Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs
TL;DR: In this article, a penalty approach to the Hamilton-Jacobi-Bellman (HJB) equation arising from the valuation of European options with proportional transaction costs is presented, where the penalty is a quasilinear 2nd-order partial differential equation with penalty parameters λ 1 and λ 2 respectively.
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