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Homework answers / question archive / Using the Blacks-Scholes Formula to find the value of a call option on the following stock: Time-to-expiration: 6 months Standard Deviation: 50% Exercise Price: $50 Stock Price: $50 Interest Rate: 3% You can find the value of N(d1) and N(d2) in the table on the last page of this assignment
Using the Blacks-Scholes Formula to find the value of a call option on the following stock:
Time-to-expiration: 6 months
Standard Deviation: 50%
Exercise Price: $50
Stock Price: $50
Interest Rate: 3%
You can find the value of N(d1) and N(d2) in the table on the last page of this assignment.
(2). What is the price of put with the same expiration date and exercise price? (Using the put-call parity)
(3). What are the deltas of the above call and put respectively?
(4). Assuming that you intend to hold the stock with a protective put. However, there is no such put available in the market. Show how can you create a synthetic protective put position without put.
Step 1: Calculate d1 & d2 from the Black Scholes formulas.
d1 = 0.217697
d2 = -0.133426
Now, from the above information, plugging into the BS formula, Call price: 7.290124
Step 2: For Put Price= C+Ke^rt - S = 7.290124 + 50*e^(-0.03*0.5) - 50 = 6.54572098
Step 3: Delta of Call = e^(-rt)*N (d1) = 0.586167
Delta of Put = Delta of Call - e^(-rt) = -0.413833
A protective put gives the principal protection similar to a call option. Hence, purchase of a call option is similar to purchase of a protective put.
A synthetic put can be created by a call + short of the stock.
