TITLE:
The Black-Scholes Merton Model—Implications for the Option Delta and the Probability of Exercise
AUTHORS:
Sunil K. Parameswaran, Sankarshan Basu
KEYWORDS:
Black-Scholes-Merton, Garman-Kohlhagen, Option Delta, Continuous Dividend Yield, Foreign Exchange Options
JOURNAL NAME:
Theoretical Economics Letters,
Vol.10 No.6,
December
25,
2020
ABSTRACT: 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.