Question

What are the deltas of a call option and a put option with the following characteristics? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

Stock price	=	$56
Exercise price	=	$55
Risk-free rate	=	4.10% per year, compounded continuously
Maturity	=	9 months
Standard deviation	=	45% per year

Call option delta
Put option delta

Answer 1

Delta measures the change in price of an option in relation to change in price of the underlying stock. Under the Black Scholes model price of a call option is computed as follows -

Call option price = S₀ * N(d1) - X * e^-rt * N(d2)

Now, Delta of a call option in the above formula is represented by -

Delta of call option = N(d1)

And, Delta of Put option = N(d1) - 1

Here is the solution -

Here are the formulae -

Therefore, Call option delta = 0.6255

Put option delta = 0.6255 - 1 = (-)0.3745