Question

# Helios' stock is currently selling for \$82.00 a share but is expected to decrease to either...

Helios' stock is currently selling for \$82.00 a share but is expected to decrease to either \$77.90 or increase to \$90.20 a share over the next year. The risk-free rate is 3 percent. What is the current value of a 1-year call option with an exercise price of \$82?

 \$4.25 \$3.95 \$3.65 \$2.75 \$0.00

Let S+ be the expected upward stock price in one year, S-, expected downward price and X be the exercise price.

Call value in 1 year, if price increases, c+ = Max(0,S+-X) = Max(0,90.2-82) = \$8.20

Call value in 1 year, if price goes down, c- = Max(0,S--X) = Max(0,77.90-82) = 0

Hedge ratio (h) = (c+-c-)/(S+-S-)

= (8.20-0)/(90.2-77.9)

= 0.66667

According to no-arbitrage approach

c = hS + PV(-hS-+c-)

Where, c is current value of call option

PV is present value factor

S is current stock price

c = 0.66667*82 + [1/(1+0.03)]*(-0.66667*77.90+0)

= 54.67-50.42

= 4.25

Therefore, the current value of 1 year call option is \$4.25

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