Dynamic Delta Hedging

Satyendra Kumar Sharma1, Arun Kumar Vaish2, Rajan Pandey3 and Charu Gupta4

Birla Institute of Technology and Science (BITS, Pilani), Vidya Vihar Campus,
Pilani – 333031, Rajasthan, India
1E-mail: satyendrasharma@bits-pilani.ac.in, 2E-mail: arunvaish@gmail.com,
3E-mail: rajan.pandey83@gmail.com, 4E-mail: charugupta@gmail.com

Abstract

Options are used by hedgers to reduce risk. A better way implemented by the companies these days is to use the delta value of options to create a portfolio having minimum risk. This portfolio has a delta value of zero. Due to the market changes the delta value changes and thus the portfolio needs to be balanced regularly. In this study, it was observed the delta value of six options of March expiry and six options of April expiry of Nifty which is traded over National Stock Exchange over the time period of 4th March to 15th April, 2010. With the help of delta values, a portfolio has been created using a call and put option of strike price Fifty One Hundred. The changes in the market over this period have been reflected in the delta values and accordingly the portfolio has been rebalanced on a per day basis. Along with this, various hypothesis regarding options have been tested. The different types of options have been analyzed and the most expensive and cheapest ones have been identified. The relation between time value of option and time of maturity has been verified. The volatility of options has been compared with market volatility and also with the strike price of respective option. These findings are explained theoretically and finally tested on the touchstone of historical data collected from the site of National Stock Exchange and values calculated with the help of standard formulae already available. The findings of the study are in consonance with the various theories about Options available. On the basis of the study conducted in furtherance of this project the author concludes that in the time period assumed, the delta neutral portfolio created was profitable for option expiring in April while was in loss for March expiry.

Keywords: Delta, Call Option, Put Option, Hedging