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European Call Option (european + call_option)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting100%

Selected Abstracts

Nonconvergence in the Variation of the Hedging Strategy of a European Call Option

MATHEMATICAL FINANCE, Issue 4 2003
R. Th.
In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order. [source]

OPTIMAL CONTINUOUS-TIME HEDGING WITH LEPTOKURTIC RETURNS

MATHEMATICAL FINANCE, Issue 2 2007

We examine the behavior of optimal mean,variance hedging strategies at high rebalancing frequencies in a model where stock prices follow a discretely sampled exponential Lévy process and one hedges a European call option to maturity. Using elementary methods we show that all the attributes of a discretely rebalanced optimal hedge, i.e., the mean value, the hedge ratio, and the expected squared hedging error, converge pointwise in the state space as the rebalancing interval goes to zero. The limiting formulae represent 1-D and 2-D generalized Fourier transforms, which can be evaluated much faster than backward recursion schemes, with the same degree of accuracy. In the special case of a compound Poisson process we demonstrate that the convergence results hold true if instead of using an infinitely divisible distribution from the outset one models log returns by multinomial approximations thereof. This result represents an important extension of Cox, Ross, and Rubinstein to markets with leptokurtic returns. [source]

Nonconvergence in the Variation of the Hedging Strategy of a European Call Option

MATHEMATICAL FINANCE, Issue 4 2003
R. Th.
In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order. [source]

Alternative tilts for nonparametric option pricing

THE JOURNAL OF FUTURES MARKETS, Issue 10 2010
M. Ryan Haley
This study generalizes the nonparametric approach to option pricing of Stutzer, M. (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie,Read family of divergence measures. Alhough the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black,Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston, S. L. (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:983,1006, 2010 [source]

Valuing credit derivatives using Gaussian quadrature: A stochastic volatility framework

THE JOURNAL OF FUTURES MARKETS, Issue 1 2004
Nabil Tahani
This article proposes semi-closed-form solutions to value derivatives on mean reverting assets. A very general mean reverting process for the state variable and two stochastic volatility processes, the square-root process and the Ornstein-Uhlenbeck process, are considered. For both models, semi-closed-form solutions for characteristic functions are derived and then inverted using the Gauss-Laguerre quadrature rule to recover the cumulative probabilities. As benchmarks, European call options are valued within the following frameworks: Black and Scholes (1973) (represents constant volatility and no mean reversion), Longstaff and Schwartz (1995) (represents constant volatility and mean reversion), and Heston (1993) and Zhu (2000) (represent stochastic volatility and no mean reversion). These comparisons show that numerical prices converge rapidly to the exact price. When applied to the general models proposed (represent stochastic volatility and mean reversion), the Gauss-Laguerre rule proves very efficient and very accurate. As applications, pricing formulas for credit spread options, caps, floors, and swaps are derived. It also is shown that even weak mean reversion can have a major impact on option prices. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:3,35, 2004 [source]