1.Alpha stock is currently trading at $34.50 a share and the 6-month call option

Question

1.Alpha stock is currently trading at $34.50 a share and the 6-month call options are at the money. The stock returns have a standard deviation of 21 percent and the risk-free rate is 4.21 percent. What is the price of the call option per share given that N(d1) is .585508 and N(d2) is .526913?

2.Today, you purchased a futures contract obligating you to purchase 100 troy ounces of gold for $1,220 per ounce any time over the next month. The current price of gold is $1,218. Assume the spot price of gold falls to $1,216 tomorrow. What will be your cash flow tomorrow for this contract?

3.Last week, you sold a futures contract on 5,000 troy ounces of silver at a settle price of $16.59. Today, your contract closed at the daily settlement price of $16.62. What amount will you receive from the contract purchaser for the delivery? Assume yesterday’s settle price was $16.66.

Explanation / Answer

1.As per BSM model Call value is given by:

Co= So. N(d1)- E/ert. N(d2)

Co= 34.50× 0.585508-34.50/e0.0421*0.5×0.526913

Co= 20.20- 17.80= 2.40

Call Price(Co)= $2.40

2. Since we have purchased the futures and prices fall down ,there is a loss,Cash outflow is given by :

(1216-1220)100= $400

3. Futures are MTM. We have to compare the today's settlement price with yesterday's settlement price to find out the cash flow.

We have short position in futures and prices fall down ,hence cash inflow of ( 16.66-16.62)×5000=$200

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