Question

A call option with an exercise price of $50 expires in six months, has a stock price of $54, and has a standard deviation of 80 percent. The risk-free rate is 9.2 percent per year annually compounded. Calculate the value of d₁.and d₂

Calculate the value of d₁

		0.3
		0.7214
		-0.7214
		0.4967

calculate the value of  d₂

+0.0690

-0.0690

+0.5657

-0.5657

Answer 1

Part A:

Step 1:

Ln (S/ X)

= Ln ( 54 / 50 )

= Ln ( 1.08)

= 0.0770

Step 2 :

d1 =[ Ln ( S/X) + [ (SD^2 / 2) + Rf ] * t ] ] / [ SD * SQRT (Time ) ]

d1 =[ 0.0770 + [ (0.8^2 / 2) + 0.092 ] * (6/12) ] ] / [ 0.8 * SQRT (6/12 ) ]

= [ 0.0770 + [ (0.64 / 2) + 0.092 ] * (6/12) ] ] / [ 0.8 * SQRT (0.5 ) ]

= [ 0.0770 + [ 0.32 + 0.092 ] * (6/12) ] ] / [ 0.8 * 0.7071 ]

= [ 0.0770 + [ 0.412 ] * (6/12) ] ] / [ 0.8 * 0.7071 ]

= [ 0.0770 + 0.206 ] / [ 0.8 * 0.7071 ]

= 0.9131 / 0.5657

= 1.6142

Part B:

d2 = d1 - [ SD * SQRT [ TIme ]

= 1.6142 - 0.5657

= 1.0485

Pls do rate, if the answer is correct and comment, if any further assistance is required.