ORMAT Math 53 – Math of Finance
Monday, March 26, 2007
Homework 5 --- Due Friday, March 30, 2007
Put-Call Parity
1. Pick a company _____________ (Despite these blanks, it might be better to report
results on a separate sheet.)
2. From the list of traded options at Yahoo!, pick…
an expiration date ______________
a strike price, K = ______________
3. Convert your expiration date to a number of years from now: T = ____________
4. Using r = 0.045, find k = Ke-rT: k = ___________________
5. Note the current price, S0 = _____________________
6. Get center prices for the put and call option with your T and K. (Center price = average of bid and asked prices; best to try this after 4:15 pm when the prices will hold still for you,
but Yahoo! hasn’t erased them yet)
Vcall = _______________
Vput = ________________
7. Is it true that Vcall – Vput = S0 – k ? Discrepancy _______________
If not, we’ll explore possible explanations:
(a) If the discrepancy is 30 cents or less, it might be just random noise
(difference between center price and “actual” market price)
(b) Early exercise premium on the put, maybe
(c) Something about dividends, maybe
The Black-Scholes formula
8. Using “BlackScholes2.xls” from the website, try to verify your call option price.
Fill in all of the yellow entries in one column. The only tricky one is the volatility;
just fill in whatever value it takes to get the spreadsheet to match your option price.
This is the “implied volatility.” In theory, it should be the same for all options on this
stock.
Implied volatility ______________
BS2 version of call option price ________________
The Valuation Grid
8. Download the “valuation.xls” workbook. Use it to estimate the value of your call option. Use the “implied volatility” from problem 8, and other data from above. Set the “call flag” to 1 (call) and the “American flag” to…well, it shouldn’t matter.
Grid version of the call option price ________________
This should agree with BS2 to within a few cents.
9. Try the same grid for valuation of the put option. Set the “call flag” to -1 and try both values (1 and 0) for the “American flag.”
Put option price if European __________________
Put option price if American __________________
Difference (extra value of American put option due to early exercise possibility) _______
The grid is probably better at estimating the difference than at estimating either version of the option in isolation.
10. Did that difference explain your discrepancy in #7 ?
11. Does your stock pay dividends?
Your prediction of the total of dividends between now and T ______________
Your estimate of the present value of all those dividends ______________
12. Does that present value explain the remaining discrepancy? The real formula should be:
(S0 – present value of dividends to T) – k = Vcall – (Vput if European).
Discrepancy in this version ____________________
(end)
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