Abstract
Correctly used financial derivatives can help investors increase their expected returns and minimize their exposure to risk. To ensure the specific needs of investors, a large number of different types of non-standard exotic options is used. Chooser option is one of them. It is an option that gives its holder the right to choose at some predetermined future time whether the option will be a standard call or put with predetermined strike price and maturity time. Although the chooser options are more expensive than standard European-style options, in many cases they are a more suitable instrument for investors in hedging their portfolio value. For an effective use of the chooser option as a hedging instrument, it is necessary to check the values of the Greek parameters delta and gamma for the options. Especially, if the value of the parameter gamma is too large, hedging of the portfolio value using only parameter delta is insufficient and brings high transaction costs because the portfolio has to be reviewed relatively often. Therefore, in this article, a modification of delta-hedging as well as using the value of parameter gamma is suggested. Error of the delta modification is analyzed and compared with the error of widely used parameter delta. Typical patterns for the modified hedging parameter variation with various time to choose time for chooser options are also presented in this article.
Highlights
The development of the financial market and growing uncertainty of its participants are the main motivation for investors to look for new financial instruments
Previous analysis shows that the sensitivity of a chooser option price to changes in the underlying asset price is evident, especially for options with underlying asset price close to the strike price
A static delta-hedging is sufficient in this case
Summary
The development of the financial market and growing uncertainty of its participants are the main motivation for investors to look for new financial instruments. A call option gives the holder the right to buy the underlying asset at the strike price before time expiration. A put option gives the holder the right to sell the underlying asset at the strike price before time expiration. If t T , the chooser option is the same as a European-style straddle, i.e. equals to the sum of the values of an European call and put option with strike price X and maturity time T. Using the properties of the Taylor expansion, we obtain the expected change in chooser option as the sum of To use this parameter in order to ensure the short position in the chooser option, holding at the long position in the underlying asset at each point in time is required. Strike price of this chooser option is $80; risk-free interest rate is 5%; volatility is 29%; and, dividend-yield is 4%
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