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https://hdl.handle.net/2142/21497
Description
Title
Rebalancing strategies for synthetic call options
Author(s)
Becker, Kent G.
Issue Date
1989
Department of Study
Business Administration
Discipline
Business Administration
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Business Administration, General
Economics, Finance
Language
eng
Abstract
This dissertation determines how well the Rubinstein-Leland (1981) synthetic option strategy replicates listed call options and theoretical Black-Scholes (BS) call premiums. Three rebalancing methods are implemented to trigger changes in the stock/debt mix: time--the portfolio is changed at fixed intervals, delta--after the delta value changes by certain percentages, and stock--when the stock changes by specified percentages. Descriptive statistics are calculated for the rebalancing errors and transactions costs for each of the strategies. The rebalancing error is equal to the difference between the synthetic call and listed call values.
This study differs from previous research because intra-day options data from the Berkeley tapes are used to test the effectiveness of the synthetic option strategy rather than simulated returns. For the sample in the study, very wide mean percentage errors result from using the BS model to replicate listed options, which call into question the effectiveness of the strategy. The mean percentage errors are approximately $-$15% to $-$20%. On average, the synthetic call option is $.43 to \$.60 greater than the listed call at rebalancing.
Another unexpected result is that the transactions cost-average error tradeoff does not hold for many of the strategies. For the delta method and, to a lesser extent, the time method, tighter rebalancing methods tend to have a lower mean percentage error, lower variance, and higher transactions costs than more liberal methods. This relationship does not hold for the stock method, due to whipsawed positions. The percentage error widens in the negative direction as the option is farther out-of-the-money and as the time to expiration increases. In addition, the variance increases as the synthetic option is farther out-of-the-money. Extremely large percentage errors can result for near maturity options, resulting in a high variance.
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