Python金融代写 | Pricing American Option with Discrete Cash Dividend


Pricing American Option with Discrete Cash Dividend

1. Project objective:
The purpose of this project is to explore and implement various option pricing
models to price American options with discrete cash dividends.

2. Background:
The incorporation of dividends in equity price models that are used to price
derivatives on an underlying stock constitutes an important and non-trivial
extension of such models. If a continuously paid dividend yield is used, or one is
willing to specify the future dividends as a fixed percentage of the stock price at
dividend dates, then the classicial option pricing model of Merton (1973), Black and
Scholes (1973) can be used with only some minor modifications, but in reality option
market makers prefer to specify dividends in terms of a fixed cash value instead of a
percentage. This destroys the very feature which makes all option pricing
computations so easy in the Black–Scholes model: the lognormal distribution of
future stock prices. Standard approximation schemes such as the Cox, Ross and
Rubinstein (1979) binomial tree methods can no longer be applied, or it becomes
extremely inefficient from a computational point of view to do so.

3. Requirement:
3.1 Starting with XOM (very liquid option)
3.2 You can use options with approximate 1-year expiry for this exercise.
3.3 You can ignore short borrow cost (these names are easy to borrow)
3.4 You can assume flat interest rate curve (constant r).
3.5 Using option data, construct American option pricing model with discrete
dividends (see reference paper)
3.6 The model should be able to handle up to four cash dividends and ex-dates
as input. The dividend amount can be identical or different.
3.7 The option pricing model should have the following inputs (option type: call
or put; stock price; interest rate; strike price; dividend (amounts and ex-
dates)) and output will be the option price

3.8 Once built the model, input some random parameters to generate the
option prices. Compare the result with option price with continuous dividend

3.9 Now assuming dividend ex-dates are known (same as data), but volatility and
dividend amount unknown. Perform calibration (optimization) to find out
the implied volatility (σ) and implied discrete dividend (d), assuming dividend
is paid at the ex-dates with amount d.

4. Data:
Options data for 4 stocks, each has 10 near the money call and 10 near the money
put with the same expiry, strike interest rate and dividends.

5. Coding Language: