Consider a non-dividend-paying stock whose current price S(0) = S is $40. After each period, there is a 60% chance that the stock price goes up by 20%. If the stock price does not go up, then it drops by 10%. A European call option and a European put option on this stock expire on the same day in 3 months at $43 strike. Current risk-free interest rate is 6% per annum, compounded continuously.
(a) Use the Black-Scholes option pricing formula to calculate the call option price after threemonths. Use Ï= lnu/(sqrt(delta t)) with u=1.20 and ât = 1/12. Use a computer algebra device to calculate N(x) for appropriate x, but you have to show manually all the components required for the formula.
Consider a non-dividend-paying stock whose current price S(0) = S is $40. After each period, there is a 60% chance that the stock price goes up by 20%. If the stock price does not go up, then it drops by 10%. A European call option and a European put option on this stock expire on the same day in 3 months at $43 strike. Current risk-free interest rate is 6% per annum, compounded continuously.
(a) Use the Black-Scholes option pricing formula to calculate the call option price after threemonths. Use Ï= lnu/(sqrt(delta t)) with u=1.20 and ât = 1/12. Use a computer algebra device to calculate N(x) for appropriate x, but you have to show manually all the components required for the formula.
Related questions
1. Company ABCâs current stock price is $68.75. The company is a small biotech company that has a new drug in the phase III of the FDCâs approval process, which is going to make a decision soon. In anticipating a big movement in the companyâs stock price, you bought 1 straddle contract (1 call contract + 1 put contract) with strike price of $67.50 and expiration in one month. You paid $7.55 for the call and $8.88 for the put.
a. Whatâs the intrinsic value of the call?
b. Whatâs the intrinsic value of the put?
c. Whatâs the time value of the call?
d. Whatâs the time value of the put?
e. If on expiration date, the stock price drops to $55 due to FDCâs decision to reject the drug, whatâs your P/L?
2. Use the Black- Scholes formula to find the value of a call option on the following stock:
Time to expiration = 6 months;
Standard deviation = 50% per year
Exercise price = $ 50
Stock price = $ 50
Interest rate = 3%
3. Find the value of a put option on the stock in the previous problem with the same exercise price and expiration as the call option.
4. 5 days ago you thought that the crude oil price was going to drop so you went ahead and sold 10 futures contracts with delivery in 5 days (which is today). The original delivery price you sold at was $52.00 per barrel. Below is how the crude oil fluctuated during the 5 days since you sold the contract:
| Day0 | $52.00 |
| Day1 | $51.76 |
| Day2 | $51.56 |
| Day3 | $52.33 |
| Day4 | $51.99 |
| Day5 | $52.33 |
a. Whatâs your total P/L?
b. Mark your account balance to market at the end of each day, assuming a 15% initial margin requirement.
