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

本次英国代写主要为python金融期权定价模型相关的project

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

yield.

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:

Python