Homework FIN 3006 2022
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Homework FIN 3006 2022
1. A four-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one month. The continuous compounding risk-free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur?(10)
2. A one-month European put option on a non-dividend-paying stock is currently selling for
$2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities are there for an arbitrageur?(8)
3. Current Stock price S(0) is $30; risk-free rate is 5%. There are two possible outcome in one year, stock price might go up 30% (to $39) or go down 30% (to $21). Consider both a call and a put with the same strike price of $30 and one year to maturity.
a. You estimate that the probability of stock price to go up is 90% and probability to go down is about 10%. Compute the price of call and put and also expected returns on the stock, call, put and a straddle (combination of a call and put with same strike of
$30) using the binomial tree model. (6)
b. However you are not sure about your estimates of the probabilities and decide to check out your results under different scenarios. You write down the following scenarios (P is the probability of stock price to go up to $39): (18)
|
P |
1-P |
call price |
put price |
Stock return |
Call return |
Put return |
Straddle return |
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0.1 |
0.9 |
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0.3 |
0.7 |
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0.5 |
0.5 |
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0.58333 5 |
0.41666 5 |
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0.7 |
0.3 |
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0.8 |
0.2 |
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0.9 |
0.1 |
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Optional question: What is your intuition on the expected returns on the call, the put and the straddle. (2)
4. Please download Tesla stock closing prices from 2021 Nov 10 to 2022 Nov 10. Suppose today is 2022 Nov 10.
a. Based on downloaded closing stock price, compute the volatility of Tesla (σ).
b. Use Libor USD one month interest rate (3.6%, monthly compounding), compute the Tesla options prices listed in the table. (Note: convert rate to continuous compounded rate). The maturity of the options is [(calendar days to expiration)/ 365]
c. Using the last option prices on the attached two figures, compute the implied volatility of options listed in the table based on Black-Scholes. (4)
TSLA, Expiration: 2022, Dec 16
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K (Strike Price) |
180 |
200 |
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50 steps Price |
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Call |
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Put |
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100 steps Price |
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Call |
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Put |
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Black Scholes Price |
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Call |
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Put |
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implied volatility |
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Call |
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Put |
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2022-11-23