45 research outputs found

    Option Pricing with Transaction Costs Using a Markov Chain Approximation

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    An e cient algorithm is developed to price European options in the pres- ence of proportional transaction costs, using the optimal portfolio frame- work of Davis (1997). A fair option price is determined by requiring that an in nitesimal diversion of funds into the purchase or sale of options has a neutral e ect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the op- tion payo into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely speci ed option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general de nition of an option hedg- ing strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

    Long-Range Dependence in Daily Interest Rate

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    We employ a number of parametric and non-parametric techniques to establish the existence of long-range dependence in daily interbank o er rates for four countries. We test for long memory using classical R=S analysis, variance-time plots and Lo's (1991) modi ed R=S statistic. In addition we estimate the fractional di erencing parameter using Whittle's (1951) maximum likelihood estimator and we shu e the data to destroy long and short memory in turn, and we repeat our non-parametric tests. From our non-parametric tests we And strong evidence of the presence of long memory in all four series independently of the chosen statistic. We nd evidence that supports the assertion of Willinger et al (1999) that Lo's statistic is biased towards non-rejection of the null hypothesis of no long-range dependence. The parametric estimation concurs with these results. Our results suggest that conventional tests for capital market integration and other similar hypotheses involving nominal interest rates should be treated with cautio

    Interpolating actions for supersymmetric quantum field theory

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    A new perturbative scheme has recently been applied to a supersymmetric quantum-field-theory model in which no conventional means for doing analytic calculations existed. We develop an alternative technique and find that it allows a very easy demonstration of the supersymmetric results: ground-state energy density E=0, and fermion-boson mass ratio R=1. Moreover, unlike other techniques, our method can be applied to models with spontaneous supersymmetry breaking, for which we illustrate the broken-supersymmetry results E0 and R1. © 1989 The American Physical Society

    Performance of utility based strategies for hedging basis risk

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    The performance of optimal strategies for hedging a claim on a non-traded asset is analyzed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation ρ\rho typically close to 1. Using a distortion method (Zariphopoulou 2001, Finance and Stochastics 5, 61-82) we derive a nonlinear expectation representation for the claim's ask price and a formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of ϵ2=1ρ2\epsilon^{2}=1-\rho^{2}. The terms in the price expansion are proportional to the central moments of the claim payoff under the minimal martingale measure. The resulting fast computation capability is used to carry out a simulation based test of the optimal hedging program, computing the terminal hedging error over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the non-traded one. The distribution of the hedging error acts as a suitable metric to analyze hedging performance. We find that the optimal policy improves hedging performance, in that the hedging error distribution is more sharply peaked around a non-negative profit. The frequency of profits over losses is increased, and this is measured by the median of the distribution, which is always increased by the optimal strategies. An empirical example illustrates the application ofthe method to the hedging of a stock basket using index futures

    A new method for the solution of the Schrodinger equation

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    We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.Comment: 4 pages, 4 figures, RevTex

    Optimal exercise of an executive stock option by an insider

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    We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. We establish conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward, and derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. Hence we show that early exercise may arise due to the agent having inside information on the future stock price

    Duality for optimal consumption under no unbounded profit with bounded risk

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