Question

For a stock with price 40, you have the following portfolio of barrier options, all expiring in 3 months: (i) An up-and-in call, barrier 45, exercise price 40.
(ii) An up-and-in call, barrier 50, exercise price 40.
(iii) An up-and-out call, barrier 45, exercise price 40.

(iv) An down-and-in call, barrier 35, exercise price 45.
(v) An down-and-in put, barrier 35, exercise price 40.
(vi) A down deferred rebate, barrier 32, payoff 5.
During the 3 month period, the minimum stock price is 31 and the maximum stock price is 47. The final price is 44.

Determine the total payoff at the end of 3 months.

Answer 1

(i) Up & In Call, Barrier 45, Exercise Price 40

Since the stock has breached the barrier of 45 it is excercisable on maturity

Payoff = (44-40) = 4

ii) Up & In Call, Barrier 50, Exercise Price 40

Since the stock has not breached the barrier it cannot be exercised

Payoff = 0

iii) An up-and-out call, barrier 45, exercise price 40

Since this is up and out call and barrier has been breached option has been knocked out

Payoff = 0

iv) An down-and-in call, barrier 35, exercise price 45.

Since stock has breached barrier it is excersiable on maturity

Payoff = Max (44-45),0

Payoff = 0 (since expired OTM)

v) An down-and-in put, barrier 35, exercise price 40.

Since stock has breached barrier it can be exercised

Payoff = Max (40-44),0

Payoff = 0 (since expired OTM)

vi) A down deferred rebate, barrier 32, payoff 5. - i dont have the subject knowledge of this kind of option