A collar is established by buying a share of stock for $50, buying a six-month p

Question

A collar is established by buying a share of stock for $50, buying a six-month put option with exercise price $45, and writing a six-month call option with exercise price $55. Based on the volatility of the stock, you calculate that for an exercise price of $45 and maturity of six months, N(d1) = .60, whereas for the exercise price of $55, N(d1) = .35.

What will be the gain or loss on the collar if the stock price increases by $1? (Input the amount as a positive value. Round your answer to 3 decimal places.)

A collar is established by buying a share of stock for $50, buying a six-month put option with exercise price $45, and writing a six-month call option with exercise price $55. Based on the volatility of the stock, you calculate that for an exercise price of $45 and maturity of six months, N(d1) = .60, whereas for the exercise price of $55, N(d1) = .35.

Explanation / Answer

Value of share of stock=$50

Exercise price of 6 month put option X=$45

Exercise price of 6 month call option Y=$55

N(d1)= Exercise price $45 of 6 month put option =0.06

N(d2)= Exercise price $55 of 6 month call option =0.35

Price increase by $1

We buy stock at $ 50

Delta=1

X=$45

N(d1)-1

=0.60-1

=-0.4

Y=$55

-N(d1)=0.35

Total=0.25

When the stock price increase by $1.than the gain in collar$0.25

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