Question

You just went long a collar involving a non-dividend-paying stock and European options on that stock. Suppose S = $40, ? = 0.30, r = 0.08, ? = 0, and T = 0.5. K(put)=$32, K(call)=$48 Compute and draw a graph with stock prices ranging from $25 to $55 depicting the profit on strategy after 1 day, 3 months, and 6 months.

Answer 1

The investor will create Collar Startgy by Buying Stock, Buying Puts and selling Call Options of underlying that stock.

The puts and the calls are both out-of-the-money options having the same expiration.

The number of underlying Stock shall remain same.

Suppose investor go long with 100 Share.

The STrike Price of Put = 32 and Stike price of Call =48,

Stock Price = 40

Risk Free Rate = 8%

Volatilty of the Stock = 30%

Time to expiry = 0.5 Years

Max Profit = Strike Price of Short Call - Purchase Price of Underlying + Net Premium Received

Max Loss = Purchase Price of Underlying - Strike Price of Long Put - Net Premium Received

Price of Put Option at K=32 = 0.3752

Price of Call Option at K=48 = 1.3376

Profit 8.9624