Math 456: Topics in Financial Mathematics
Prof. Wickerhauser
Fall, 2022


FINAL PROJECT

Choose a publicly traded company that offers a dividend and let XYZ be
its common stock.  One of the stocks listed among the Standard and
Poors 100 (S&P100) is a good choice as these are heavily traded with
widely published data.

Use US Treasury T-Bill discount rates to estimate riskless returns.

Analyze contingent claims on XYZ in various ways:

1. Find the implied volatility sigma(K,T) of XYZ using options at
various near-the-money strike prices K and near-future expiry dates T.
Justify your choice of options.  Use both CRR and Black-Scholes
pricing models and compare the results.  Also compare your results to
published implied volatilities and comment on any differences.  Plot
the implied volatility surface sigma(K,T) for your results.

2. Choose a time to expiry T that includes at least two dividend
payments expected to equal the most recent.  Use the CRR model for
American-style options with dividend to price Call and Put options
with expiry T at various near-the-money strike prices.  What
volatility should be used?  How do your prices compare with the market
prices for these options?  How would your prices change if the second
dividend was 20% higher than the first?

3. Choose a time to expiry T that contains no expected dividends.
Construct an implied binomial tree from the spot price and at least
five near-the-money Call option premiums on XYZ with expiry T.  Use it
to price five near-the-money Put options on XYZ with the same expiry
T.  Compare your results with the market prices of those Puts and also
with the values given by the Call-Put parity formula.


Submit your work electronically.  Cite any software that you use.  Show
any software that you write.  Your work will be judged for its clarity
as well as for its completeness.