Author(s)

Sunil K. Parameswaran¹, Sankarshan Basu²

¹Tarheel Consultancy Services, Bangalore, India.
²Indian Institute of Management Bangalore, Bangalore, India.

This paper analyzes the implications of the Black-Scholes-Merton model of option pricing, for the deltas of call and put options and their respective probabilities of exercise at expiration. It derives a threshold value of the stock price and shows that in certain cases the options will have a delta in excess of 0.50, and will also have more than a 50% probability of exercise, while other options will have a delta that is lower than 0.50 and a probability of exercise that is lower than 50%. Similar results are obtained for the Garman-Kohlhagen model, which is an extension of the Black-Scholes Merton model, for valuing foreign currency options.

Black-Scholes-Merton, Garman-Kohlhagen, Option Delta, Continuous Dividend Yield, Foreign Exchange Options

Parameswaran, S. and Basu, S. (2020) The Black-Scholes Merton Model
—Implications for the Option Delta and the Probability of Exercise. Theoretical Economics Letters, 10, 1307-1313. doi: 10.4236/tel.2020.106080.