Question

A collar is established by buying a share of stock for $50, buying a 6-month put option with exercise price $43, and writing a 6-month call option with exercise price $57. On the basis of the volatility of the stock, you calculate that for a strike price of $43 and expiration of 6 months, N(d1) = 0.8235, whereas for the exercise price of $57, N(d1) = 0.7411. a. What will be the gain or loss on the collar if the stock price increases by $1?

Answer 1

The gain on collar is $0.0824

Step-by-step explanation:

Given Data;

6-month put option exercise price = $43

writing a 6-month call option exercise price = $57

Value of share of stock = $50

N(d1) = strike price of $43 and expiration of 6 months =0.8235

N(d1) =the exercise price of $57 = 0.7411

Position Delta

Buy stock, $50 1

Buy put, $43 N(d1)-1

= 0.8235-1

= - 0.1765

Write call, $57 -N(d1)

= -0.7411

Total $0.0824

Therefore, when the price increased by $1, the gain on collar is $0.0824

Answer 2

$0.0824

Step-by-step explanation:

Calculating the gain on the collar, we have:

Gain= (delta of stock)- (delta of call) + (delta of put)

Where,

Delta of call = N(d1) short call=0.7411

Delta of put = (N(d1) long put - 1) =

0.8235 - 1 = -0.1765

Therefore gain will be:

Gain = $1 - 0.7411 - 0.1765

= 0.0824

The gain on the collar by an increase of $1 in stock price is 0.0824