Question

The value of the S&P500 stock index is 1,000. The risk-free interest rate is 3% per annum with continuous compounding. The dividend yield on the S&P 500 is 1%, and the volatility of the index is 20% per annum. Find the delta on a 6 months put option with strike price 950. Interpret your result.

Answer 1

Underlying Price : 1000

Exercise Price : 950

Days Until Expiration : 180

Interest Rates : 3%

Dividend Yield : 1%

Volatility : 20%

Call Option	Put Option
Theoretical Price	88.608	29.576
Delta	0.693	-0.307
Gamma	0.002	0.002
Vega	2.465	2.465
Theta	-0.186	-0.109
Rho	2.966	-1.65

Delta for the Put option will always be between -1 and 0, here it is -0.307, shows the option has 30% chances to finish up in the money, in other words the Put option will make money has only 30% chances.